%PDF-1.3
%âãÏÓ
1 0 obj
<<
/Width 1
/Filter[/CCITTFaxDecode]
/ImageMask true
/Subtype/Image
/Type/XObject
/Length 4
/BitsPerComponent 1
/Decode[1 0]
/Height 1
/DecodeParms[<>]
>>
stream
€ €endstream
endobj
2 0 obj
<<
/Length 2523
>>
stream
/GS4 gs
BT
/F0 1 Tf
8.96638 0 0 8.96638 144 716.4 Tm
0 g
[(Revist)67(a)-361(de)-374(Ma)67(tem)]TJ
9.27465 0.0803 TD
<13>Tj
-0.02677 -0.0803 TD
[(atica:)-481(Teor)]TJ
5.98235 0.0803 TD
<13>Tj
0.12045 -0.0803 TD
[<1061>-361(y)-374(Aplica)27(ciones)-374(2010)]TJ
/F1 1 Tf
11.77733 0 Td
(17)Tj
/F0 1 Tf
1.17773 0 Td
[((1))-374(:)-495(1{12)]TJ
-28.30575 -1.51232 TD
(cimp)Tj
2.14133 -0.00001 TD
[(a)-361({)-388(ucr)-2261(issn:)-495(1409-2433)]TJ
/F2 1 Tf
17.21544 0 0 17.21544 173.16 615.48 Tm
[(algebraic)-384(jet)-377(sp)70(a)21(ces)-370(and)-378(zilber)71('s)]TJ
3.78497 -1.26863 TD
[(dichotomy)-379(in)-376(dcf)90(a)]TJ
-3.86862 -4.56567 TD
[(esp)70(a)21(cios)-377(de)-377(jets)-369(algebraicos)-385(y)-377(la)]TJ
1.3941 -1.2756 TD
(dicotom)Tj
4.00106 0.08365 TD
<13>Tj
0.12547 -0.08365 TD
[<1061>-384(de)-376(zilber)-382(en)-377(dcf)90(a)]TJ
/F3 1 Tf
11.95517 0 0 11.95517 224.28 457.32 Tm
[(R)30(onald)-382(F.)-382(Bust)70(amante)-372(Medina)]TJ
/F4 1 Tf
7.97011 0 0 7.97011 412.44 461.64 Tm
<03>Tj
/F5 1 Tf
11.95517 0 0 11.95517 154.68 421.92 Tm
[(R)51(e)50(c)51(eive)51(d:)-442(15)-351(Apr)-351(2009;)-341(R)51(evise)52(d:)-442(16)-341(Oct)-351(2009;)-341(A)50(c)51(c)50(epte)51(d:)-452(21)-341(Oct)]TJ
12.6874 -1.13424 TD
(2009)Tj
ET
q
340.20001 0 0 -0.6 148.188 384.468 cm
/Im1 Do
Q
BT
/F6 1 Tf
10.90909 0 0 10.90909 144 342.12 Tm
[(Keyw)33(ords:)]TJ
/F7 1 Tf
5.962 0 Td
[(Mo)-33(del)-407(Theory)-396(of)-407(Fields,)-429(Sup)-33(ersimple)-374(Theories,)-429(Di\013erence-)]TJ
-5.962 -1.243 TD
[(Di\013eren)33(tial)-363(Fields,)-341(De\fnable)-341(Sets.)]TJ
/F6 1 Tf
0 -1.793 TD
[(P)33(alabras)-451(cla)33(v)33(e:)]TJ
/F7 1 Tf
8.173 0 Td
[(T)88(eor)110<13>385<1061>-396(de)-385(mo)-33(delos,)-396(teor)110<13>]TJ
10.439 0 Td
[(\020as)-407(sup)-33(ersimples,)-374(camp)-33(os)-385(dife-)]TJ
-18.61199 -1.243 TD
[(renciales)-341(de)-341(diferencia,)-341(conjun)33(tos)-330(de\fnibles.)]TJ
/F6 1 Tf
0 -1.793 TD
[(Mathematics)-385(Sub)-66(ject)-385(Classi\fcation:)]TJ
/F7 1 Tf
18.557 0 Td
[(11U09,)-352(12H05,)-363(12H10)]TJ
ET
q
113.4 0 0 -0.6 160.908 187.908 cm
/Im1 Do
Q
BT
/F8 1 Tf
5.97758 0 0 5.97758 156.24 173.52 Tm
<03>Tj
/F9 1 Tf
8.96638 0 0 8.96638 160.56 169.68 Tm
[(CIMP)81(A,)-335(Escuela)-334(de)-322(Matem\023)510(atica,)-346(Univ)26(ersidad)-321(de)-308(Costa)-346(Rica,)-334(2060)-333(San)-322(Jos)28<13>]TJ
33.37803 0 Td
[(e,)-348(Costa)]TJ
-35.22493 -1.21788 TD
[(Rica.)-468(E-Mail:)]TJ
/F10 1 Tf
6.57122 0 Td
(ronald.bustamte@emate.ucr.ac.cr)Tj
/F7 1 Tf
10.90909 0 0 10.90909 315.6 128.88 Tm
(1)Tj
ET
endstream
endobj
3 0 obj
<<
/SA false
/Type/ExtGState
>>
endobj
4 0 obj
<<
/Length 6980
>>
stream
/GS4 gs
BT
/F7 1 Tf
10.90909 0 0 10.90909 144 722.16 Tm
0 g
(2)Tj
/F11 1 Tf
7.37 0 Td
[(R.)-374(Busamante)]TJ
/F12 1 Tf
5.97758 0 0 5.97758 309.72 722.16 Tm
[(R)60(ev.Mate.T)80(e)60(or.Aplic.)]TJ
/F13 1 Tf
11.4829 0 Td
((2010))Tj
/F14 1 Tf
3.7741 0 Td
(17)Tj
/F15 1 Tf
1.40525 0 Td
((1))Tj
/F16 1 Tf
9.96264 0 0 9.96264 296.4 686.4 Tm
(Abstract)Tj
/F17 1 Tf
-11.05731 -1.6863 TD
[(This)-422(is)-410(the)-422(\frst)-423(of)-421(t)23(w)25(o)-410(pap)-24(ers)-410(dev)24(oted)-409(to)-422(the)-422(pro)-24(of)-410(of)-422(Zilb)-24(er's)]TJ
-1.50563 -1.19245 TD
[(dic)24(hotom)24(y)-217(for)-217(the)-241(case)-217(of)-216(di\013erence-di\013eren)24(tial)-230(\felds)-229(of)-217(c)25(haracteristic)]TJ
0 -1.2045 TD
[(zero.)-710(In)-422(this)-423(pap)-24(er)-422(w)25(e)-422(use)-421(the)-422(tec)24(hniques)-422(exp)-24(osed)-421(in)-422([9])-422(to)-421(pro)23(v)24(e)]TJ
0 -1.20451 TD
[(a)-494(w)25(eak)24(er)-470(v)24(ersion)-482(of)-494(the)-506(dic)24(hotom)24(y)84(,)-518(more)-494(precisely)85(,)-530(w)24(e)-481(pro)23(v)24(e)-481(the)]TJ
0 -1.19245 TD
[(follo)24(wing:)-506(in)]TJ
/F18 1 Tf
5.89 0 Td
[(DCF)96(A)]TJ
/F17 1 Tf
3.1317 0 Td
[(the)-374(canonical)-348(base)-362(of)-373(a)-361(\fnite-dimensional)-362(t)23(yp)-24(e)]TJ
-9.0217 -1.2045 TD
[(is)-302(in)24(ternal)-301(to)-302(the)-313(\fxed)-301(\feld)-313(of)-301(the)-314(\feld)-313(of)-301(constan)24(ts.)-423(This)-301(will)-313(imply)]TJ
T*
[(a)-421(w)24(eak)-397(v)24(ersion)-398(of)-422(Zilb)-24(er's)-422(dic)24(hotom)24(y:)-603(a)-409(\fnite-dimensional)-411(t)24(yp)-24(e)-421(of)]TJ
/F19 1 Tf
0 -1.19245 TD
0.061 Tc
(SU)Tj
/F17 1 Tf
1.46949 0 Td
0 Tc
[(-rank)-374(1)-385(is)-386(either)-386(1-based)-374(or)-374(non-orthogonal)-362(to)-386(the)-385(\fxed)-398(\feld)-385(of)]TJ
-1.46949 -1.2045 TD
[(the)-337(\feld)-338(of)-337(constan)24(ts.)]TJ
/F16 1 Tf
12.46657 -2.25241 TD
(Resumen)Tj
/F17 1 Tf
-10.96095 -1.67426 TD
[(El)-493(presen)23(te)-494(es)-494(el)-493(primero)-483(de)-505(dos)-495(art)108<13>385(\020culos)-470(dedicados)-481(a)-494(la)-506(de-)]TJ
-1.50563 -1.2045 TD
[(mostraci\023)505(on)-458(de)-469(la)-458(dicotom)109<13>385<1061>-446(de)-469(Zilb)-25(er)-469(para)-446(el)-470(caso)-458(de)-469(los)-458(camp)-24(os)]TJ
T*
[(difernciales)-289(de)-301(diferencia)-289(de)-301(caracter)108<13>386(\020stica)-254(cero.)-421(En)-264<13>469(este)-277(art)108<13>385(\020culo)-276(uti-)]TJ
0 -1.19245 TD
[(lizamos)-313(las)-314(t)24<13>470(ecnicas)-313(desarrolladas)-278(en)-325([9])-326(para)-301(demostrar)-303(una)-325(v)24(ersi\023)506(on)]TJ
0 -1.2045 TD
[(d)24<13>470(ebil)-409(de)-410(la)-397(dicotom)108<13>386(\020a:)-578(un)-410(tip)-25(o)-421(de)-409(dimensi\023)505(on)-409(\fnita)-410(y)-410(de)-409(rango)]TJ
/F19 1 Tf
28.06485 0 Td
0.061 Tc
(SU)Tj
/F17 1 Tf
-28.06485 -1.19245 TD
0 Tc
[(igual)-470(a)-457(1)-470(es)-470(mo)-24(dular)-458(o)-470(no)-457(ortogonal)-447(al)-469(camp)-24(o)-458(\fjo)-470(del)-481(camp)-24(o)-458(de)]TJ
0 -1.2045 TD
[(constan)24(tes.)]TJ
/F20 1 Tf
14.34624 0 0 14.34624 144 428.88 Tm
[(1)-1130(In)33(tro)-34(duction)-378(and)-368(preliminaries)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 144 404.52 Tm
[(The)-286(theory)-286(of)-297(di\013eren)33(tially)-308(closed)-297(\felds)-286(\()]TJ
/F21 1 Tf
(DCF)Tj
/F7 1 Tf
[(\))-297(is)-286(the)-297(mo)-33(del)-286(companion)-286(of)]TJ
0 -1.232 TD
[(the)-264(theory)-264(of)-275(di\013eren)33(tial)-275(\felds.)-418(Among)-264(the)-264(prop)-33(erties)-264(of)]TJ
/F21 1 Tf
24.40899 0 Td
(DCF)Tj
/F7 1 Tf
2.387 0 Td
[(w)33(e)-264(\fnd)-253(that)]TJ
-26.796 -1.243 TD
[(it)-275(is)]TJ
/F22 1 Tf
1.87 0 Td
(!)Tj
/F7 1 Tf
0.66 0 Td
[(-stable,)-286(it)-275(eliminates)-275(quan)33(ti\fers)-264(and)-264(imaginaries.)-429(An)-264(axiomatization)]TJ
-2.53 -1.243 TD
(for)Tj
/F21 1 Tf
1.529 0 Td
(DCF)Tj
/F7 1 Tf
2.453 0 Td
[(is)-341(the)-330(follo)33(wing.)]TJ
/F6 1 Tf
-3.982 -1.958 TD
[(De\fnition)-385(1.1)]TJ
/F21 1 Tf
7.337 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.628 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(D)]TJ
/F7 1 Tf
2.541 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.66 0 Td
[(b)55(e)-253(a)-264(di\013er)55(ential)-264(\feld.)]TJ
/F22 1 Tf
9.35 0 Td
(K)Tj
/F21 1 Tf
1.177 0 Td
[(is)-264(di\013er)55(ential)-55(ly)-264(close)55(d)]TJ
-22.69299 -1.243 TD
[(if)-407(and)-429(only)-418(if)]TJ
/F22 1 Tf
6.281 0 Td
(K)Tj
/F21 1 Tf
1.331 0 Td
[(is)-418(an)-418(algebr)55(aic)55(al)-55(ly)-429(close)55(d)-429(\feld)-418(and)-429(for)-418(every)-418(irr)55(e)55(ducible)]TJ
-7.612 -1.243 TD
[(algebr)55(aic)-429(variety)]TJ
/F22 1 Tf
7.612 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
0.44 Tc
[(,i)440(f)]TJ
/F22 1 Tf
1.782 0 Td
0 Tc
(W)Tj
/F21 1 Tf
1.507 0 Td
[(is)-418(an)-429(irr)55(e)55(ducible)-429(algebr)55(aic)-429(subvariety)-429(of)]TJ
/F22 1 Tf
17.798 0 Td
<1C>Tj
/F23 1 Tf
7.97011 0 0 7.97011 470.64 313.8 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 475.44 315.48 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F21 1 Tf
-31.56999 -1.243 TD
[(such)-308(that)-330(the)-319(pr)55(oje)55(ction)-330(of)]TJ
/F22 1 Tf
11.561 0 Td
(W)Tj
/F21 1 Tf
1.386 0 Td
(onto)Tj
/F22 1 Tf
2.233 0 Td
(V)Tj
/F21 1 Tf
1.111 0 Td
[(is)-308(dominant,)-341(then)-319(ther)55(e)-319(is)]TJ
/F22 1 Tf
11.418 0 Td
(a)Tj
/F24 1 Tf
0.803 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\()Tj
/F22 1 Tf
(K)Tj
/F7 1 Tf
1.309 0 Td
(\))Tj
/F21 1 Tf
-31.56999 -1.232 TD
[(such)-363(that)]TJ
/F7 1 Tf
4.323 0 Td
(\()Tj
/F22 1 Tf
[(a;)-165(D)-33(a)]TJ
/F7 1 Tf
(\))Tj
/F24 1 Tf
3.41 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(W)Tj
/F21 1 Tf
1.089 0 Td
(.)Tj
/F7 1 Tf
-9.768 -1.958 TD
[(This)-308(axiomatization)-352(is)-308(not)-319(the)-319(original)-330(and)-308(most)-319(kno)33(wn,)-308(but)-308(this)-319(v)33(ersion,)]TJ
0 -1.243 TD
[(due)-363(to)-385(Pierce)-385(and)-363(Pilla)33(y)-396(\([7)-11(]\),)-385(has)-374(a)-374(more)-374(geometric)-396(spirit)-374(whic)33(h)-374(will)-374(b)-33(e)]TJ
T*
[(useful)-330(in)-330(this)-330(pap)-33(er.)]TJ
1.551 -1.243 TD
[(A)-319(consequence)-319(of)]TJ
/F22 1 Tf
7.81 0 Td
(!)Tj
/F7 1 Tf
0.66 0 Td
[(-stabilit)33(y)-341(is)-308(Zilb)-33(er's)-308(dic)33(hotom)33(y)-330(for)]TJ
/F21 1 Tf
15.125 0 Td
(DCF)Tj
/F7 1 Tf
0.319 Tc
[(:A)11(t)352(y)319(p)286(eo)319(f)]TJ
/F22 1 Tf
-25.146 -1.243 TD
0 Tc
(U)Tj
/F7 1 Tf
0.792 0 Td
[(-rank)-407(1)-407(is)-407(either)-407(one-based)-407(or)-407(nonorthogonal)-407(to)-418(the)-407(\feld)-396(of)-407(constan)33(ts.)]TJ
-0.792 -1.243 TD
[(Pro)-33(ofs)-330(and)-330(details)-341(ab)-33(out)]TJ
/F21 1 Tf
11.11 0 Td
(DCF)Tj
/F7 1 Tf
2.453 0 Td
[(can)-341(b)-33(e)-330(found)-319(in)-330([6)-11(])-330(and)-330([5)-11(].)]TJ
-12.012 -2.475 TD
[(The)-242(theory)-242(of)-242(di\013erence-di\013eren)33(tial)-264(\felds)-242(of)-242(c)33(haracteristic)-275(zero)-253(also)-253(has)]TJ
-1.551 -1.243 TD
[(a)-451(mo)-33(del-companion,)-495(\()]TJ
/F21 1 Tf
-0.022 Tc
[(AC)-22(F)77(A)]TJ
/F7 1 Tf
12.529 0 Td
0 Tc
[(\).)-451(It)-451(is)-451(sup)-33(ersimple,)-462(quan)33(ti\fer-free)]TJ
/F22 1 Tf
15.884 0 Td
(!)Tj
/F7 1 Tf
0.66 0 Td
(-stable)Tj
ET
endstream
endobj
5 0 obj
<<
/Length 9978
>>
stream
/GS4 gs
BT
/F11 1 Tf
10.90909 0 0 10.90909 170.88 722.16 Tm
0 g
[(algebraic)-363(jet)-363(sp)66(a)22(ces)-363(and)-363(zilber)66('s)-363(dichotomy)-363(in)-385(dcf)88(a)]TJ
/F7 1 Tf
28.99599 0 Td
(3)Tj
-31.45999 -3.278 TD
[(and)-374(it)-396(eliminates)-396(imaginaries.)-616(It)-385(do)-33(es)-374(not)-385(eliminate)-407(quan)33(ti\fers)-385(and)-374(it)-385(is)]TJ
0 -1.243 TD
[(not)-462(a)-462(complete)-484(theory)88(,)-495(but)-451(its)-462(completions)-473(are)-473(easily)-473(describ)-33(ed.)-803(Since)]TJ
/F21 1 Tf
T*
-0.022 Tc
[(AC)-22(F)77(A)]TJ
/F7 1 Tf
3.069 0 Td
0 Tc
[(is)-352(sup)-33(ersimple,)-330(its)-352(complete)-363(t)33(yp)-33(es)-352(are)-352(rank)33(ed)-341(b)33(y)-352(the)]TJ
/F22 1 Tf
23.21 0 Td
0.055 Tc
(SU)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
[(-rank.)-484(As)]TJ
/F21 1 Tf
-27.74199 -1.243 TD
(DCF)Tj
/F7 1 Tf
2.123 0 Td
(,)Tj
/F21 1 Tf
0.693 0 Td
-0.022 Tc
[(AC)-22(F)77(A)]TJ
/F7 1 Tf
3.146 0 Td
0 Tc
[(satis\fes)-418(Zilb)-33(er's)-407(dic)33(hotom)33(y:)-627(a)-418(t)33(yp)-33(e)-418(of)]TJ
/F22 1 Tf
17.314 0 Td
0.055 Tc
(SU)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
[(-rank)-407(1)-418(is)-418(either)]TJ
-24.73899 -1.243 TD
[(1-based)-418(or)-429(non-orthogonal)-429(to)-429(the)-418(\fxed)-407(\feld.)-704(See)-418([3)-11(])-418(for)-418(pro)-33(ofs)-407(of)-418(these)]TJ
(facts.)'
1.551 -1.243 TD
[(The)-341(original)-363(pro)-33(ofs)-341(of)-352(these)-352(t)33(w)33(o)-363(dic)33(hotomies)-374(ha)33(v)33(e)-363(a)-352(hea)33(vy)-352(use)-352(of)-352(sta-)]TJ
-1.551 -1.24299 TD
[(bilit)33(y)-319(\(or)-308(simplicit)33(y\),)-330(but)-308(recen)33(tly)-319(Pilla)33(y)-319(and)-297(Zigler)-319(found)-286(more)-308(geometric)]TJ
T*
[(pro)-33(ofs)-275(using)-286(algebraic)-297(jet)-297(spaces.)-429(One)-286(imp)-33(ortan)33(t)-286(fact)-297(whic)33(h)-286(is)-286(k)33(ey)-286(to)-297(b)-33(oth)]TJ
T*
[(pro)-33(ofs)-396(is)-407(that)-418(ha)33(ving)-418(\fnite)-407(transcendence)-407(degree)-418(and)-396(ha)33(ving)-418(\fnite)-407(rank)]TJ
0 -1.23199 TD
[(are)-341(equiv)55(alen)33(t)-352(in)-330(b)-33(oth)]TJ
/F21 1 Tf
9.944 0 Td
(DCF)Tj
/F7 1 Tf
2.464 0 Td
(and)Tj
/F21 1 Tf
1.936 0 Td
-0.022 Tc
[(AC)-22(F)77(A)]TJ
/F7 1 Tf
2.739 0 Td
0 Tc
(.)Tj
-15.532 -1.243 TD
[(Hrusho)33(vski)-451(pro)33(v)33(ed)-462(that)-462(the)-451(theory)-462(of)-451(di\013erence-di\013eren)33(tial)-484(\felds)-440(of)]TJ
-1.551 -1.243 TD
[(c)33(haracteristic)-495(zero)-462(has)-462(a)-462(mo)-33(del-companion.)-836(W)88(e)-473(denote)-462(it)]TJ
/F21 1 Tf
26.50999 0 Td
[(DCF)99(A)]TJ
/F7 1 Tf
[(.)-451(This)]TJ
-26.50999 -1.243 TD
[(theory)-286(is)-286(sup)-33(ersimple,)-275(quan)33(ti\fer-free)]TJ
/F22 1 Tf
16.148 0 Td
(!)Tj
/F7 1 Tf
0.66 0 Td
[(-stable,)-308(and)-275(it)-286(eliminates)-297(imaginar-)]TJ
-16.808 -1.243 TD
[(ies.)-693(Pro)-33(ofs)-407(of)-418(these)-418(facts)-429(are)-418(found)-396(in)-418([1)-11(].)-693(As)]TJ
/F21 1 Tf
21.065 0 Td
[(DCF)99(A)]TJ
/F7 1 Tf
3.179 0 Td
[(is)-418(sup)-33(ersimple)-396(its)]TJ
-24.244 -1.24299 TD
[(t)33(yp)-33(es)-363(are)-374(rank)33(ed)-363(b)33(y)-374(the)]TJ
/F22 1 Tf
10.868 0 Td
0.055 Tc
(SU)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
[(-rank,)-374(in)-363([2)-11(])-363(the)-374(author)-363(pro)33(v)33(ed)-374(that)-374(the)]TJ
/F22 1 Tf
17.831 0 Td
0.055 Tc
(SU)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
(-)Tj
-31.62499 -1.243 TD
[(rank)-297(of)-319(a)-308(mo)-33(del)-308(of)]TJ
/F21 1 Tf
8.261 0 Td
[(DCF)99(A)]TJ
/F7 1 Tf
3.069 0 Td
[(\(that)-319(is,)-319(the)]TJ
/F22 1 Tf
5.489 0 Td
0.055 Tc
(SU)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
[(-rank)-308(of)-308(a)-308(di\013erence-di\013eren)33(tial)]TJ
-18.28199 -1.243 TD
[(transcenden)33(tal)-363(elemen)33(t\))-374(is)]TJ
/F22 1 Tf
11.847 0 Td
(!)Tj
/F23 1 Tf
7.97011 0 0 7.97011 280.44 459.96 Tm
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 285.12 456 Tm
[(,)-363(and)-341(giv)33(es)-374(an)-352(example)-363((3.1))-363(of)-363(a)-352(set)-363(whose)]TJ
/F22 1 Tf
-12.936 -1.243 TD
0.055 Tc
(SU)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
[(-rank)-330(1)-341(but)-330(has)-330(in\fnite)-330(transcendence)-330(degree.)]TJ
/F20 1 Tf
14.34624 0 0 14.34624 144 408.36 Tm
[(2)-1130(Algebraic)-378(jet)-385(spaces)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 144 384 Tm
[(W)88(e)-418(list)-418(the)-418(main)-407(prop)-33(erties)-407(of)-407(jet)-418(spaces)-407(o)33(v)33(er)-429(algebraically)-440(closed)-418(\felds)]TJ
0 -1.243 TD
[(of)-363(c)33(haracteristic)-385(zero.)-528(W)88(e)-374(will)-352(supp)-33(ose)-341(all)-374(v)55(arieties)-374(to)-363(b)-33(e)-352(absolutely)-363(irre-)]TJ
(ducible.)'
/F6 1 Tf
0 -1.947 TD
[(De\fnition)-385(2.1)]TJ
/F21 1 Tf
7.337 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.793 0 Td
0 Tc
(K)Tj
/F21 1 Tf
1.342 0 Td
[(b)55(e)-418(an)-418(algebr)55(aic)55(al)-55(ly)-440(close)55(d)-440(\feld)-418(,)-440(and)-429(let)]TJ
/F22 1 Tf
17.886 0 Td
(V)Tj
/F24 1 Tf
1.199 0 Td
<12>Tj
/F25 1 Tf
1.166 0 Td
(A)Tj
/F26 1 Tf
7.97011 0 0 7.97011 487.08 339.6 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 144 322.2 Tm
[(b)55(e)-363(a)-374(variety)-374(over)]TJ
/F22 1 Tf
7.678 0 Td
(K)Tj
/F26 1 Tf
7.97011 0 0 7.97011 237.84 326.16 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 243.36 322.2 Tm
[(;)-374(let)]TJ
/F22 1 Tf
2.09 0 Td
(a)Tj
/F21 1 Tf
0.902 0 Td
[(b)55(e)-363(a)-374(non)-374(singular)-374(p)55(oint)-374(of)]TJ
/F22 1 Tf
11.66 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
0.484 Tc
[(.L)539(e)484(t)]TJ
/F24 1 Tf
2.53 0 Td
0 Tc
(O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 448.2 320.52 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 465 322.2 Tm
0 Tc
[(b)55(e)-363(the)]TJ
-29.425 -1.243 TD
[(lo)55(c)55(al)-374(ring)-363(of)]TJ
/F22 1 Tf
5.533 0 Td
(V)Tj
/F21 1 Tf
1.166 0 Td
(at)Tj
/F22 1 Tf
1.199 0 Td
(a)Tj
/F21 1 Tf
0.891 0 Td
[(and)-363(let)]TJ
/F27 1 Tf
3.344 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 287.76 306.96 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 304.44 308.64 Tm
0 Tc
[(b)55(e)-363(its)-352(maximal)-385(ide)55(al.)]TJ
-13.156 -1.243 TD
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.76 0 Td
0.341 Tc
(m>)Tj
/F7 1 Tf
2.332 0 Td
0 Tc
(0)Tj
/F21 1 Tf
[(.)-572(The)]TJ
/F22 1 Tf
3.454 0 Td
(m)Tj
/F21 1 Tf
[(-th)-385(jet)-396(sp)55(ac)55(e)-407(of)]TJ
/F22 1 Tf
7.81 0 Td
(V)Tj
/F21 1 Tf
1.199 0 Td
(at)Tj
/F22 1 Tf
1.232 0 Td
(a)Tj
/F21 1 Tf
(,)Tj
/F22 1 Tf
1.232 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 375.48 299.04 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 383.52 295.08 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 400.8 293.4 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 405.84 295.08 Tm
[(,)-396(is)-385(the)-407(dual)-396(sp)55(ac)55(e)]TJ
-24.002 -1.243 TD
[(of)-363(the)]TJ
/F22 1 Tf
2.838 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-ve)55(ctor)-352(sp)55(ac)55(e)]TJ
/F27 1 Tf
5.907 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 260.88 279.84 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 273.72 281.52 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 290.52 286.08 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 309.48 281.52 Tm
0 Tc
(.)Tj
/F6 1 Tf
-15.169 -2.189 TD
[(Notation)-374(2.2)]TJ
/F21 1 Tf
6.82 0 Td
[(If)-352(the)-363(variety)]TJ
/F22 1 Tf
6.039 0 Td
(V)Tj
/F21 1 Tf
1.166 0 Td
(is)Tj
/F25 1 Tf
1.067 0 Td
(A)Tj
/F26 1 Tf
7.97011 0 0 7.97011 316.56 261.6 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 322.2 257.64 Tm
[(,)-363(we)-352(write)]TJ
/F27 1 Tf
4.686 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 384.72 255.96 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 393.72 257.64 Tm
[(inste)55(ad)-374(of)]TJ
/F27 1 Tf
4.576 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 455.04 255.96 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 467.88 257.64 Tm
0 Tc
(.)Tj
/F7 1 Tf
-29.689 -2.2 TD
[(The)-330(follo)33(wing)-352(is)-330(pro)33(v)33(ed)-341(in)-330([9)-11(])-330(\(F)88(act)-363(1.2\).)]TJ
/F6 1 Tf
0 -2.189 TD
[(F)99(act)-385(2.3)]TJ
/F21 1 Tf
4.499 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.991 0 Td
0 Tc
[(U;)-165(V)]TJ
/F21 1 Tf
2.563 0 Td
[(b)55(e)-627(irr)55(e)55(ducible)-638(varieties)-638(of)]TJ
/F22 1 Tf
12.364 0 Td
(K)Tj
/F26 1 Tf
7.97011 0 0 7.97011 387.72 213.72 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 393.36 209.76 Tm
(,)Tj
/F22 1 Tf
1.001 0 Td
(a)Tj
/F24 1 Tf
1.298 0 Td
(2)Tj
/F22 1 Tf
1.43 0 Td
(V)Tj
/F24 1 Tf
1.221 0 Td
(\\)Tj
/F22 1 Tf
1.089 0 Td
(U)Tj
/F21 1 Tf
0.792 0 Td
1.276 Tc
[(.I)1276(f)]TJ
/F22 1 Tf
-29.68899 -1.243 TD
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 151.08 200.16 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 159.12 196.2 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 176.28 194.52 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 184.44 196.2 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 203.04 200.16 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 210.96 196.2 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(U)Tj
/F7 1 Tf
0.792 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 228 194.52 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 237 196.2 Tm
[(for)-363(al)-55(l)]TJ
/F22 1 Tf
3.025 0 Td
0.275 Tc
(m>)Tj
/F7 1 Tf
2.211 0 Td
0 Tc
(0)Tj
/F21 1 Tf
[(,)-363(then)]TJ
/F22 1 Tf
3.388 0 Td
(V)Tj
/F7 1 Tf
1.089 0 Td
(=)Tj
/F22 1 Tf
1.056 0 Td
(U)Tj
/F21 1 Tf
0.792 0 Td
(.)Tj
/F6 1 Tf
-20.086 -2.189 TD
[(Prop)-33(osition)-396(2.4)]TJ
/F21 1 Tf
8.184 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.76 0 Td
0 Tc
(V)Tj
/F21 1 Tf
1.188 0 Td
[(b)55(e)-385(an)-396(variety,)]TJ
/F22 1 Tf
6.391 0 Td
(a)Tj
/F21 1 Tf
0.913 0 Td
[(a)-396(non-singular)-396(p)55(oint)-396(of)]TJ
/F22 1 Tf
10.505 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
0.539 Tc
[(.L)594(e)539(t)]TJ
/F24 1 Tf
-29.74399 -1.243 TD
0 Tc
(O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 152.64 157.08 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 164.4 158.76 Tm
[(b)55(e)-627(the)-627(lo)55(c)55(al)-638(ring)-627(of)]TJ
/F22 1 Tf
9.746 0 Td
(V)Tj
/F21 1 Tf
1.419 0 Td
(at)Tj
/F22 1 Tf
1.463 0 Td
(a)Tj
/F21 1 Tf
[(,)-693(and)]TJ
/F27 1 Tf
3.729 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 354.24 157.08 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 373.8 158.76 Tm
0 Tc
[(its)-627(maximal)-638(ide)55(al.)-1265(L)55(et)]TJ
ET
endstream
endobj
6 0 obj
<<
/Length 16316
>>
stream
/GS4 gs
BT
/F7 1 Tf
10.90909 0 0 10.90909 144 722.16 Tm
0 g
(4)Tj
/F11 1 Tf
7.37 0 Td
[(R.)-374(Busamante)]TJ
/F12 1 Tf
5.97758 0 0 5.97758 309.72 722.16 Tm
[(R)60(ev.Mate.T)80(e)60(or.Aplic.)]TJ
/F13 1 Tf
11.4829 0 Td
((2010))Tj
/F14 1 Tf
3.7741 0 Td
(17)Tj
/F15 1 Tf
1.40525 0 Td
((1))Tj
/F24 1 Tf
10.90909 0 0 10.90909 144 686.4 Tm
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 157.08 684.72 Tm
0.061 Tc
[(V;)61(a)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 174.48 686.4 Tm
0 Tc
(=)Tj
/F24 1 Tf
1.188 0 Td
(f)Tj
/F22 1 Tf
(f)Tj
/F24 1 Tf
1.518 0 Td
(2)Tj
/F22 1 Tf
1.089 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
0.275 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
0.418 Tc
(]:)Tj
/F22 1 Tf
1.397 0 Td
0 Tc
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
0.418 Tc
(\)=0)Tj
/F24 1 Tf
3.41 0 Td
0 Tc
(g)Tj
/F21 1 Tf
0.935 0 Td
[(b)55(e)-440(the)-440(maximal)-462(ide)55(al)-440(of)-440(the)-440(c)55(o)55(or)55(dinate)]TJ
-14.938 -1.243 TD
[(ring)-330(of)]TJ
/F22 1 Tf
3.223 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.078 0 Td
(])Tj
/F21 1 Tf
0.616 0 Td
(of)Tj
/F22 1 Tf
1.144 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(.)-451(Then,)-341(for)-330(al)-55(l)]TJ
/F22 1 Tf
6.622 0 Td
(m)Tj
/F24 1 Tf
1.155 0 Td
(2)Tj
/F25 1 Tf
0.946 0 Td
(N)Tj
/F21 1 Tf
(,)Tj
/F24 1 Tf
1.364 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 352.08 671.16 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 364.8 672.84 Tm
0 Tc
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 383.28 676.8 Tm
(m)Tj
0 -0.90337 TD
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 399.72 672.84 Tm
0 Tc
(and)Tj
/F27 1 Tf
1.914 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 432 671.16 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 444.84 672.84 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 461.64 676.8 Tm
(m)Tj
0 -0.90337 TD
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 478.08 672.84 Tm
0 Tc
[(ar)55(e)]TJ
-30.62399 -1.243 TD
[(isomorphic)-385(K-ve)55(ctor)-363(sp)55(ac)55(es)-374(.)]TJ
/F11 1 Tf
0 -2.134 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
[(This)-319(is)-330(a)-330(consequence)-341(from)-319(the)-341(fact)-330(that)]TJ
/F24 1 Tf
17.952 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 369.84 626.4 Tm
(i)Tj
0 -0.90337 TD
(a;V)Tj
/F24 1 Tf
10.90909 0 0 10.90909 386.28 622.44 Tm
(\\)Tj
/F22 1 Tf
0.88 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.078 0 Td
0.286 Tc
(]=)Tj
/F27 1 Tf
1.617 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 446.76 626.4 Tm
(i)Tj
0 -0.90337 TD
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 464.52 622.44 Tm
[(for)-330(all)]TJ
/F22 1 Tf
-29.38099 -1.243 TD
(i)Tj
/F7 1 Tf
[(.)-451(\(cf)-341(Prop)-33(osition)-330(2.2)-352(in)-330([4]\))-341(.)]TJ
/F28 1 Tf
13.2 0 Td
(2)Tj
/F7 1 Tf
-11.649 -1.243 TD
[(The)-330(follo)33(wing)-352(fact)-341(is)-341(pro)33(v)33(ed)-330(in)-330([10)-11(],)-341(Chapter)-330(I)-33(I,)-330(section)-341(5.)]TJ
/F6 1 Tf
-1.551 -2.123 TD
[(F)99(act)-385(2.5)]TJ
/F21 1 Tf
4.499 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.782 0 Td
0 Tc
[(U;)-165(V)]TJ
/F21 1 Tf
2.343 0 Td
[(b)55(e)-418(two)-418(irr)55(e)55(ducible)-429(varieties)-418(de\fne)55(d)-429(over)]TJ
/F22 1 Tf
17.897 0 Td
(L)Tj
/F24 1 Tf
1.056 0 Td
<12>Tj
/F22 1 Tf
1.155 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
0.627 Tc
[(.L)682(e)627(t)]TJ
/F22 1 Tf
-29.65599 -1.24299 TD
0 Tc
(f)Tj
/F7 1 Tf
0.935 0 Td
(:)Tj
/F22 1 Tf
0.616 0 Td
(U)Tj
/F24 1 Tf
1.122 0 Td
(!)Tj
/F22 1 Tf
1.342 0 Td
(V)Tj
/F21 1 Tf
1.188 0 Td
[(b)55(e)-396(a)-396(\fnite)-385(morphism,)-429(and)-396(let)]TJ
/F22 1 Tf
13.2 0 Td
(b)Tj
/F24 1 Tf
0.77 0 Td
(2)Tj
/F22 1 Tf
1.001 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
0.55 Tc
[(.I)550(f)]TJ
/F22 1 Tf
1.947 0 Td
0 Tc
(f)Tj
/F21 1 Tf
0.99 0 Td
[(is)-385(unr)55(ami\fe)55(d)-418(at)]TJ
/F22 1 Tf
7.315 0 Td
(b)Tj
/F21 1 Tf
0.429 0 Td
(,)Tj
-31.65799 -1.24299 TD
[(then,)-440(for)-429(any)]TJ
/F22 1 Tf
6.248 0 Td
(a)Tj
/F24 1 Tf
0.913 0 Td
(2)Tj
/F22 1 Tf
1.056 0 Td
(f)Tj
/F4 1 Tf
7.97011 0 0 7.97011 240.24 549 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 251.52 545.04 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(b)Tj
/F7 1 Tf
0.429 0 Td
(\))Tj
/F21 1 Tf
0.814 0 Td
[(and)-429(for)-429(any)-429(p)55(ositive)-429(inte)55(ger)]TJ
/F22 1 Tf
12.672 0 Td
(m)Tj
/F21 1 Tf
[(,)-429(the)-429(homomor-)]TJ
-24.156 -1.24299 TD
(phism)Tj
/F7 1 Tf
3.124 0.264 TD
<16>Tj
/F22 1 Tf
-0.209 -0.264 TD
(f)Tj
/F7 1 Tf
0.869 0 Td
(:)Tj
/F24 1 Tf
0.561 0 Td
(O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 200.04 529.68 Tm
0.061 Tc
[(V;)61(b)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 211.92 531.48 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 228.72 535.44 Tm
(m)Tj
0 -0.91843 TD
0.061 Tc
[(V;)61(b)]TJ
/F24 1 Tf
10.90909 0 0 10.90909 243.72 531.48 Tm
0.275 Tc
(!O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 266.28 529.8 Tm
-0.015 Tc
[(U;)-15(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 279.36 531.48 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 296.16 535.44 Tm
(m)Tj
0 -0.90337 TD
-0.015 Tc
[(U;)-15(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 313.2 531.48 Tm
0 Tc
[(induc)55(e)55(d)-363(by)]TJ
/F22 1 Tf
4.906 0 Td
(f)Tj
/F21 1 Tf
0.957 0 Td
[(is)-352(an)-363(isomorphism.)]TJ
/F6 1 Tf
-21.373 -2.134 TD
[(Prop)-33(osition)-396(2.6)]TJ
/F21 1 Tf
8.184 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
2.09 0 Td
0 Tc
[(U;)-165(V)]TJ
/F21 1 Tf
2.662 0 Td
[(b)55(e)-715(two)-737(irr)55(e)55(ducible)-737(varieties)-726(de\fne)55(d)-737(over)]TJ
/F22 1 Tf
-12.936 -1.24299 TD
(L)Tj
/F24 1 Tf
1.155 0 Td
<12>Tj
/F22 1 Tf
1.254 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
0.77 Tc
[(.L)825(e)770(t)]TJ
/F22 1 Tf
2.915 0 Td
0 Tc
(f)Tj
/F7 1 Tf
1.067 0 Td
(:)Tj
/F22 1 Tf
0.759 0 Td
(U)Tj
/F24 1 Tf
1.254 0 Td
(!)Tj
/F22 1 Tf
1.474 0 Td
(V)Tj
/F21 1 Tf
1.276 0 Td
[(b)55(e)-462(a)-473(dominant)-484(generic)55(al)-55(ly)-473(\fnite-to-one)-473(mor-)]TJ
-12.078 -1.24299 TD
[(phism.)-539(L)55(et)]TJ
/F22 1 Tf
5.137 0 Td
(a)Tj
/F21 1 Tf
0.902 0 Td
[(b)55(e)-385(a)-385(generic)-374(of)]TJ
/F22 1 Tf
6.842 0 Td
(U)Tj
/F21 1 Tf
1.177 0 Td
(over)Tj
/F22 1 Tf
2.233 0 Td
(L)Tj
/F21 1 Tf
[(.)-517(Then)]TJ
/F22 1 Tf
4.136 0 Td
(f)Tj
/F21 1 Tf
0.979 0 Td
[(induc)55(es)-385(an)-385(isomorphism)]TJ
-21.406 -1.243 TD
(of)Tj
/F22 1 Tf
1.177 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-ve)55(ctor)-352(sp)55(ac)55(es)-385(b)55(etwe)55(en)]TJ
/F22 1 Tf
9.977 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 282.84 471.48 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 290.88 467.52 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(U)Tj
/F7 1 Tf
0.792 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 307.92 465.84 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 316.8 467.52 Tm
(and)Tj
/F22 1 Tf
1.947 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 345.12 471.48 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 353.16 467.52 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 370.32 465.36 Tm
(f)Tj
/F23 1 Tf
0.61731 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 386.88 467.52 Tm
(.)Tj
/F11 1 Tf
-22.264 -2.123 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
(Since)Tj
/F22 1 Tf
2.684 0 Td
(f)Tj
/F7 1 Tf
1.001 0 Td
[(is)-396(separable)-407(\(as)-407(w)33(e)-407(w)33(ork)-407(in)-396(c)33(haracteristic)-440(zero\),)-429(and)-396(since)]TJ
/F22 1 Tf
26.12499 0 Td
(f)Tj
/F7 1 Tf
-31.36099 -1.243 TD
[(is)-429(dominan)33(t)-440(and)]TJ
/F22 1 Tf
7.722 0 Td
(f)Tj
/F4 1 Tf
7.97011 0 0 7.97011 234.84 421.2 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 246.12 417.24 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
[(\)\))-440(is)-429(\fnite,)]TJ
/F22 1 Tf
5.797 0 Td
(U)Tj
/F7 1 Tf
1.221 0 Td
(and)Tj
/F22 1 Tf
2.046 0 Td
(V)Tj
/F7 1 Tf
1.243 0 Td
[(are)-440(irreducible)-429(and)-418(their)]TJ
-21.043 -1.243 TD
[(dimensions)-440(are)-451(equal,)-484(th)33(us)]TJ
/F22 1 Tf
12.397 0 Td
(f)Tj
/F7 1 Tf
1.034 0 Td
[(is)-451(unrami\fed)-429(at)]TJ
/F22 1 Tf
7.579 0 Td
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
[(\).)-781(By)-462(2.5,)]TJ
/F22 1 Tf
6.072 0 Td
(f)Tj
/F7 1 Tf
1.045 0 Td
(induces)Tj
-28.73199 -1.243 TD
[(an)-319(isomorphism)-308(b)-33(et)33(w)33(een)]TJ
/F24 1 Tf
11.055 0 Td
(O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 273.24 387.84 Tm
0.061 Tc
[(V;)61(f)]TJ
/F23 1 Tf
1.59596 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F22 1 Tf
10.90909 0 0 10.90909 297.48 390.12 Tm
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 314.28 394.68 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.06899 TD
0.061 Tc
[(V;)61(f)]TJ
/F23 1 Tf
1.59596 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F7 1 Tf
10.90909 0 0 10.90909 342.24 390.12 Tm
(and)Tj
/F24 1 Tf
1.925 0 Td
(O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 371.88 388.44 Tm
-0.015 Tc
[(U;)-15(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 384.96 390.12 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 401.76 394.68 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
-0.015 Tc
[(U;)-15(a)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 420.6 390.12 Tm
0 Tc
[(;)-330(whose)-319(restric-)]TJ
-25.355 -1.529 TD
[(tion)-363(to)]TJ
/F27 1 Tf
3.333 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 191.76 371.16 Tm
0.061 Tc
[(V;)61(f)]TJ
/F23 1 Tf
1.59596 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F22 1 Tf
10.90909 0 0 10.90909 216 373.44 Tm
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 232.8 378 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.06899 TD
0.061 Tc
[(V;)61(f)]TJ
/F23 1 Tf
1.59596 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F7 1 Tf
10.90909 0 0 10.90909 261.12 373.44 Tm
[(is)-363(an)-352(isomorphism)-352(b)-33(et)33(w)33(een)]TJ
/F27 1 Tf
12.199 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 405.6 371.16 Tm
0.061 Tc
[(V;)61(f)]TJ
/F23 1 Tf
1.59596 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F22 1 Tf
10.90909 0 0 10.90909 429.96 373.44 Tm
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 446.76 378 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.06899 TD
0.061 Tc
[(V;)61(f)]TJ
/F23 1 Tf
1.59596 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F7 1 Tf
10.90909 0 0 10.90909 475.08 373.44 Tm
(and)Tj
/F27 1 Tf
-30.349 -1.529 TD
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 155.4 355.08 Tm
-0.015 Tc
[(U;)-15(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 168.48 356.76 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 185.28 361.32 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
-0.015 Tc
[(U;)-15(a)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 204.12 356.76 Tm
0 Tc
[(.)-594(Then,)-385(b)33(y)-385(2.1,)]TJ
/F22 1 Tf
7.205 0 Td
(f)Tj
/F7 1 Tf
0.979 0 Td
[(induces)-374(an)-385(isomorphism)-374(b)-33(et)33(w)33(een)]TJ
/F22 1 Tf
14.85 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 462.48 360.72 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 470.52 356.76 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(U)Tj
/F7 1 Tf
0.792 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 487.56 355.08 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 144 343.2 Tm
(and)Tj
/F22 1 Tf
1.947 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 172.32 347.16 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 180.24 343.2 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 197.52 341.04 Tm
(f)Tj
/F23 1 Tf
0.61731 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F7 1 Tf
10.90909 0 0 10.90909 214.08 343.2 Tm
(.)Tj
/F28 1 Tf
0.726 0 Td
(2)Tj
/F7 1 Tf
-7.15 -1.243 TD
[(The)-352(follo)33(wing)-374(lemma)-374(\(2.3)-374(of)-363([9)-11(]\))-363(allo)33(ws)-374(us)-352(to)-374(consider)-352(jet)-363(spaces)-374(as)-363(alge-)]TJ
T*
[(braic)-341(v)55(arieties.)]TJ
/F6 1 Tf
0 -2.123 TD
[(Lemma)-385(2.7)]TJ
/F21 1 Tf
6.05 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.727 0 Td
0 Tc
(K)Tj
/F21 1 Tf
1.276 0 Td
[(b)55(e)-352(an)-363(algebr)55(aic)55(al)-55(ly)-385(close)55(d)-374(\feld)-363(and)]TJ
/F22 1 Tf
15.323 0 Td
(V)Tj
/F21 1 Tf
1.155 0 Td
[(a)-363(subvariety)-363(of)]TJ
/F22 1 Tf
-25.53099 -1.243 TD
(K)Tj
/F26 1 Tf
7.97011 0 0 7.97011 154.08 283.32 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 163.56 279.36 Tm
[(,)-363(let)]TJ
/F22 1 Tf
2.068 0 Td
(m)Tj
/F24 1 Tf
1.155 0 Td
(2)Tj
/F6 1 Tf
0.946 0 Td
(N)Tj
/F21 1 Tf
1.265 0 Td
[(and)-363(let)]TJ
/F24 1 Tf
3.344 0 Td
(D)Tj
/F21 1 Tf
1.155 0 Td
[(b)55(e)-363(the)-363(set)-352(of)-363(op)55(er)55(ators)]TJ
/F7 1 Tf
1.155 -1.782 TD
(1)Tj
ET
q
43.08 0 0 -0.48 265.788 255.468 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 265.8 245.04 Tm
(s)Tj
/F23 1 Tf
7.97011 0 0 7.97011 270.96 243.36 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 275.64 245.04 Tm
(!)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.331 0 Td
0 Tc
(s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 300.12 243.36 Tm
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 305.76 245.04 Tm
(!)Tj
/F22 1 Tf
2.739 1.364 TD
(@)Tj
/F26 1 Tf
7.97011 0 0 7.97011 342 263.88 Tm
(s)Tj
ET
q
59.76 0 0 -0.48 311.148 255.468 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 311.16 245.04 Tm
0.055 Tc
(@x)Tj
/F26 1 Tf
7.97011 0 0 7.97011 323.76 249.96 Tm
0 Tc
(s)Tj
/F13 1 Tf
5.97758 0 0 5.97758 327.72 248.88 Tm
(1)Tj
/F23 1 Tf
7.97011 0 0 7.97011 323.76 241.92 Tm
(1)Tj
/F24 1 Tf
10.90909 0 0 10.90909 334.2 245.04 Tm
0.165 Tc
<010101>Tj
/F22 1 Tf
1.331 0 Td
0.055 Tc
(@x)Tj
/F26 1 Tf
7.97011 0 0 7.97011 361.32 249.84 Tm
0 Tc
(s)Tj
/F29 1 Tf
5.97758 0 0 5.97758 365.28 248.88 Tm
(n)Tj
/F26 1 Tf
7.97011 0 0 7.97011 361.32 243.6 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 144 224.64 Tm
[(wher)55(e)]TJ
/F7 1 Tf
2.827 0 Td
(0)Tj
/F22 1 Tf
0.77 0 Td
0.275 Tc
(Tj
/F7 1 Tf
1.386 0 Td
0 Tc
(+)Tj
/F22 1 Tf
1.001 0 Td
(s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 342 222.96 Tm
(n)Tj
/F22 1 Tf
10.90909 0 0 10.90909 347.52 224.64 Tm
0.451 Tc
(;s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 360.6 222.96 Tm
0 Tc
(i)Tj
/F24 1 Tf
10.90909 0 0 10.90909 366.96 224.64 Tm
<15>Tj
/F7 1 Tf
1.056 0 Td
(0)Tj
/F21 1 Tf
0.495 0 Td
(.)Tj
-20.43799 -1.243 TD
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.727 0 Td
0 Tc
(a)Tj
/F7 1 Tf
0.803 0 Td
0.275 Tc
(=\()Tj
/F22 1 Tf
1.441 0 Td
0 Tc
(a)Tj
/F23 1 Tf
7.97011 0 0 7.97011 210 209.4 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 214.8 211.08 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
(;a)Tj
/F26 1 Tf
7.97011 0 0 7.97011 246.6 209.4 Tm
0 Tc
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 252.24 211.08 Tm
(\))Tj
/F24 1 Tf
0.671 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(;)-352(and)-374(let)]TJ
/F22 1 Tf
4.015 0 Td
(d)Tj
/F7 1 Tf
0.792 0 Td
(=)Tj
/F24 1 Tf
1.056 0 Td
[(jD)-33(j)]TJ
/F21 1 Tf
(.)Tj
-16.654 -1.243 TD
[(Then)-363(we)-363(c)55(an)-363(identify)]TJ
/F22 1 Tf
9.559 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 272.28 201.48 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 280.32 197.52 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 297.48 195.84 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 306.48 197.52 Tm
(with)Tj
/F24 1 Tf
-9.075 -2.189 TD
(f)Tj
/F7 1 Tf
0.495 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(c)Tj
/F26 1 Tf
7.97011 0 0 7.97011 221.76 171.84 Tm
(h)Tj
/F7 1 Tf
10.90909 0 0 10.90909 227.28 173.64 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 231.48 171.84 Tm
(h)Tj
/F4 1 Tf
0.61731 0 Td
(2D)Tj
/F24 1 Tf
10.90909 0 0 10.90909 252.36 173.64 Tm
(2)Tj
/F22 1 Tf
0.946 0 Td
(K)Tj
/F26 1 Tf
7.97011 0 0 7.97011 272.76 178.2 Tm
(d)Tj
/F7 1 Tf
10.90909 0 0 10.90909 280.56 173.64 Tm
(:)Tj
/F30 1 Tf
0.627 0.957 TD
(X)Tj
/F26 1 Tf
7.97011 0 0 7.97011 286.68 160.32 Tm
(h)Tj
/F4 1 Tf
0.61731 0 Td
(2D)Tj
/F22 1 Tf
10.90909 0 0 10.90909 305.76 173.64 Tm
0.033 Tc
(DP)Tj
/F7 1 Tf
1.639 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
0.913 0 Td
(\))Tj
/F22 1 Tf
(c)Tj
/F26 1 Tf
7.97011 0 0 7.97011 342.48 171.84 Tm
(h)Tj
/F7 1 Tf
10.90909 0 0 10.90909 351 173.64 Tm
0.275 Tc
(=0)Tj
/F22 1 Tf
1.551 0 Td
0.451 Tc
(;P)Tj
/F24 1 Tf
1.793 0 Td
0 Tc
(2)Tj
/F22 1 Tf
0.946 0 Td
(I)Tj
/F7 1 Tf
0.517 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F24 1 Tf
0.385 0 Td
(g)Tj
/F22 1 Tf
(:)Tj
ET
endstream
endobj
7 0 obj
<<
/Length 16034
>>
stream
/GS4 gs
BT
/F11 1 Tf
10.90909 0 0 10.90909 170.88 722.16 Tm
0 g
[(algebraic)-363(jet)-363(sp)66(a)22(ces)-363(and)-363(zilber)66('s)-363(dichotomy)-363(in)-385(dcf)88(a)]TJ
/F7 1 Tf
28.99599 0 Td
(5)Tj
/F11 1 Tf
-31.45999 -3.278 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.287 TD
(Let)Tj
/F22 1 Tf
2.167 0 Td
(p)Tj
/F7 1 Tf
1.408 0 Td
(:)Tj
/F22 1 Tf
1.188 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
(X)Tj
/F7 1 Tf
1.177 0 Td
(])Tj
/F24 1 Tf
1.188 0 Td
-0.165 Tc
<0021>Tj
/F22 1 Tf
2.519 0 Td
0 Tc
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.078 0 Td
[(])-715(suc)33(h)-704(that)]TJ
/F22 1 Tf
6.171 0 Td
0.077 Tc
[(Ke)77(r)]TJ
/F7 1 Tf
1.87 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(p)Tj
/F7 1 Tf
0.902 Tc
(\)=)Tj
/F22 1 Tf
3.861 0 Td
0 Tc
(I)Tj
/F7 1 Tf
0.517 0 Td
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.199 0 Td
[(\))-715(;)-902(then)]TJ
/F22 1 Tf
-27.74199 -1.243 TD
(p)Tj
/F4 1 Tf
7.97011 0 0 7.97011 149.52 662.76 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 160.8 658.8 Tm
(\()Tj
/F24 1 Tf
0.385 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 178.08 657.1201 Tm
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 192.36 658.8 Tm
0.539 Tc
(\)=)Tj
/F24 1 Tf
2.233 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 229.8 657.1201 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 234.84 658.8 Tm
[(,)-528(and)]TJ
/F22 1 Tf
2.904 0 Td
(p)Tj
/F4 1 Tf
7.97011 0 0 7.97011 272.04 662.76 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 283.32 658.8 Tm
(\()Tj
/F24 1 Tf
0.385 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 300.6 663.36 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.99371 TD
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 319.44 658.8 Tm
0.539 Tc
(\)=)Tj
/F24 1 Tf
2.244 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 357 662.76 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.82809 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 379.32 658.8 Tm
(+)Tj
/F22 1 Tf
1.111 0 Td
(I)Tj
/F7 1 Tf
0.517 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
[(\).)-924(This)-473(giv)33(es)-506(us)]TJ
-24.38699 -1.243 TD
[(the)-341(follo)33(wing)-341(short)-330(exact)-352(sequence:)]TJ
0.418 -2.354 TD
(0)Tj
/F24 1 Tf
0.781 0 Td
-0.176 Tc
<0021>Tj
/F7 1 Tf
1.881 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(I)Tj
/F7 1 Tf
0.902 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
0.231 Tc
(\)+)Tj
/F24 1 Tf
1.617 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 231.24 624 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.90337 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 250.08 619.56 Tm
(\))Tj
/F22 1 Tf
0.385 0 Td
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 272.76 624 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.90337 TD
(a)Tj
/F24 1 Tf
10.90909 0 0 10.90909 294.72 619.56 Tm
-0.176 Tc
[<0021>-451(M)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 328.32 617.88 Tm
0 Tc
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 333.36 619.56 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 351.84 624 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.90337 TD
(a)Tj
/F24 1 Tf
10.90909 0 0 10.90909 373.8 619.56 Tm
-0.176 Tc
[<0021>-462(M)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 407.52 617.88 Tm
0 Tc
(a;V)Tj
/F22 1 Tf
10.90909 0 0 10.90909 421.68 619.56 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 440.16 624.12 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
(a;V)Tj
/F24 1 Tf
10.90909 0 0 10.90909 462 619.56 Tm
-0.165 Tc
<0021>Tj
/F7 1 Tf
1.892 0 Td
0 Tc
(0)Tj
-29.49099 -2.541 TD
[(W)88(e)-308(pro)-33(ceed)-286(to)-308(describ)-33(e)-286(the)-286(dual)-297(space)-297(of)]TJ
/F24 1 Tf
17.941 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 369.72 590.16 Tm
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 374.76 591.84 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 393.24 595.8 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 412.08 591.84 Tm
[(:)-429(The)-286(monomials)]TJ
-24.574 -1.243 TD
(\()Tj
/F22 1 Tf
0.385 0 Td
(X)Tj
/F24 1 Tf
1.089 0 Td
<00>Tj
/F22 1 Tf
0.957 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 180.48 582.2401 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 187.92 578.28 Tm
0.275 Tc
(=\()Tj
/F22 1 Tf
1.441 0 Td
0 Tc
(X)Tj
/F24 1 Tf
1.089 0 Td
<00>Tj
/F22 1 Tf
0.957 0 Td
(a)Tj
/F23 1 Tf
7.97011 0 0 7.97011 231.72 576.6 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 236.52 578.28 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 240.72 582.2401 Tm
(s)Tj
/F13 1 Tf
5.97758 0 0 5.97758 244.68 581.16 Tm
(1)Tj
/F24 1 Tf
10.90909 0 0 10.90909 251.04 578.28 Tm
0.165 Tc
<010101>Tj
/F7 1 Tf
1.342 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.385 0 Td
(X)Tj
/F24 1 Tf
1.089 0 Td
<00>Tj
/F22 1 Tf
0.946 0 Td
(a)Tj
/F26 1 Tf
7.97011 0 0 7.97011 297.84 576.6 Tm
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 303.48 578.28 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 307.68 582.2401 Tm
(s)Tj
/F29 1 Tf
5.97758 0 0 5.97758 311.64 581.28 Tm
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 320.64 578.28 Tm
[(with)-308(1)]TJ
/F24 1 Tf
3.036 0 Td
<14>Tj
/F22 1 Tf
1.056 0 Td
(s)Tj
/F23 1 Tf
7.97011 0 0 7.97011 370.44 576.6 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 377.04 578.28 Tm
(+)Tj
/F24 1 Tf
0.957 0 Td
0.165 Tc
<010101>Tj
/F7 1 Tf
1.342 0 Td
0 Tc
(+)Tj
/F22 1 Tf
0.957 0 Td
(s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 417.72 576.6 Tm
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 426.36 578.28 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
(s)Tj
/F24 1 Tf
0.748 0 Td
<14>Tj
/F22 1 Tf
1.056 0 Td
(m)Tj
/F7 1 Tf
1.188 0 Td
(form)Tj
-29.93099 -1.243 TD
[(a)-352(basis)-352(for)]TJ
/F24 1 Tf
4.862 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 210.12 563.04 Tm
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 215.16 564.72 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 233.64 568.68 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 252.48 564.72 Tm
[(,)-363(and)-341(for)-341(eac)33(h)]TJ
/F22 1 Tf
6.402 0 Td
(s)Tj
/F7 1 Tf
0.814 0 Td
-0.033 Tc
[(we)-396(h)-33(ave)-396(a)]TJ
/F22 1 Tf
4.664 0 Td
0 Tc
(K)Tj
/F7 1 Tf
0.924 0 Td
[(-linear)-352(map)]TJ
/F22 1 Tf
5.357 0 Td
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 456.84 563.04 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 465.12 564.72 Tm
[(whic)33(h)]TJ
-29.436 -1.243 TD
[(assigns)-330(1)-319(to)-330(\()]TJ
/F22 1 Tf
5.753 0 Td
(X)Tj
/F24 1 Tf
1.111 0 Td
<00>Tj
/F22 1 Tf
0.979 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 239.52 555.12 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 247.56 551.16 Tm
[(and)-308(0)-330(to)-330(the)-330(other)-319(monomials.)-451(The)-319(maps)]TJ
/F22 1 Tf
18.315 0 Td
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 453.6 549.48 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 461.52 551.16 Tm
[(form)-319(a)]TJ
-29.106 -1.243 TD
[(basis)-330(for)-330(the)-341(dual)-330(of)]TJ
/F24 1 Tf
9.064 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 255.96 535.92 Tm
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 261 537.6 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 279.48 541.56 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 298.44 537.6 Tm
(.)Tj
-12.606 -1.287 TD
[(Th)33(us,)-308(the)-297(dual)]TJ
/F22 1 Tf
6.677 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 240.84 527.52 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 248.88 523.56 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 266.04 521.88 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 274.44 523.56 Tm
(of)Tj
/F24 1 Tf
1.111 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 299.64 521.88 Tm
(a;V)Tj
/F22 1 Tf
10.90909 0 0 10.90909 313.8 523.56 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 332.28 528.2401 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 351.12 523.56 Tm
[(,)-319(consists)-308(of)-308(those)-308(linear)-308(maps)]TJ
/F22 1 Tf
-18.986 -1.43 TD
(u)Tj
/F7 1 Tf
0.847 0 Td
(:)Tj
/F24 1 Tf
0.561 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 172.44 506.28 Tm
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 177.48 507.96 Tm
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 195.96 511.92 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.84315 TD
(a)Tj
/F24 1 Tf
10.90909 0 0 10.90909 217.8 507.96 Tm
-0.165 Tc
<0021>Tj
/F22 1 Tf
1.892 0 Td
0 Tc
(K)Tj
/F7 1 Tf
1.254 0 Td
[(that)-341(tak)33(e)-352(the)-330(v)55(alue)-341(0)-341(on)-330(\()]TJ
/F22 1 Tf
(I)Tj
/F7 1 Tf
11.759 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
0.231 Tc
(\)+)Tj
/F24 1 Tf
1.617 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 424.2 506.28 Tm
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 438.36 507.96 Tm
(\))Tj
/F22 1 Tf
0.385 0 Td
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 461.04 512.52 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 480 507.96 Tm
(.)Tj
-29.24899 -1.287 TD
(Let)Tj
/F22 1 Tf
1.892 0 Td
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
(X)Tj
/F7 1 Tf
1.287 0 Td
(\))Tj
/F24 1 Tf
0.825 0 Td
(2)Tj
/F22 1 Tf
1.1 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
0.275 0 Td
(X)Tj
/F7 1 Tf
0.902 0 Td
[(];)-495(applying)-429(T)88(a)33(ylor's)-440(form)33(ula)-429(w)33(e)-440(can)-429(write,)-462(mo)-33(dulo)]TJ
/F24 1 Tf
-9.361 -1.243 TD
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 157.08 484.92 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.99371 TD
(a;V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 175.92 480.36 Tm
(,)Tj
/F22 1 Tf
4.433 -1.716 TD
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(X)Tj
/F7 1 Tf
0.902 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.22 Tc
(\)+)Tj
/F30 1 Tf
2.948 0.957 TD
0 Tc
(X)Tj
/F23 1 Tf
7.97011 0 0 7.97011 297.84 447.84 Tm
(1)Tj
/F4 1 Tf
0.52697 0 Td
<146A>Tj
/F26 1 Tf
1.12922 0 Td
(s)Tj
/F4 1 Tf
0.49686 0 Td
<6A14>Tj
/F26 1 Tf
1.12922 0 Td
(m)Tj
/F22 1 Tf
10.90909 0 0 10.90909 333.24 461.64 Tm
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 342.24 459.96 Tm
(s)Tj
/F22 1 Tf
10.90909 0 0 10.90909 346.68 461.64 Tm
(f)Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(X)Tj
/F24 1 Tf
1.133 0 Td
<00>Tj
/F22 1 Tf
1.001 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 404.88 466.2 Tm
(s)Tj
/F22 1 Tf
10.90909 0 0 10.90909 409.32 461.64 Tm
(;)Tj
/F7 1 Tf
-22.77 -3.102 TD
(where)Tj
/F22 1 Tf
7.887 -1.573 TD
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 255.96 408.96 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 263.4 410.64 Tm
(=)Tj
2.882 0.671 TD
(1)Tj
ET
q
43.08 0 0 -0.48 276.108 413.628 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 276.12 403.2 Tm
(s)Tj
/F23 1 Tf
7.97011 0 0 7.97011 281.28 401.52 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 285.96 403.2 Tm
(!)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.342 0 Td
0 Tc
(s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 310.56 401.52 Tm
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 316.08 403.2 Tm
(!)Tj
/F22 1 Tf
3.08 1.353 TD
(@)Tj
/F26 1 Tf
7.97011 0 0 7.97011 356.04 421.92 Tm
(s)Tj
ET
q
67.08 0 0 -0.48 321.468 413.628 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 321.48 403.2 Tm
0.055 Tc
(@X)Tj
/F26 1 Tf
7.97011 0 0 7.97011 337.68 408 Tm
0 Tc
(s)Tj
/F13 1 Tf
5.97758 0 0 5.97758 341.64 406.92 Tm
(1)Tj
/F23 1 Tf
7.97011 0 0 7.97011 336.84 400.08 Tm
(1)Tj
/F24 1 Tf
10.90909 0 0 10.90909 348.24 403.2 Tm
0.165 Tc
<010101>Tj
/F22 1 Tf
1.331 0 Td
0.055 Tc
(@X)Tj
/F26 1 Tf
7.97011 0 0 7.97011 378.96 407.88 Tm
0 Tc
(s)Tj
/F29 1 Tf
5.97758 0 0 5.97758 382.92 406.92 Tm
(n)Tj
/F26 1 Tf
7.97011 0 0 7.97011 378.12 401.76 Tm
(n)Tj
/F7 1 Tf
10.90909 0 0 10.90909 160.92 381.6 Tm
(If)Tj
/F22 1 Tf
0.957 0 Td
(u)Tj
/F7 1 Tf
0.847 0 Td
(=)Tj
/F30 1 Tf
1.056 0.748 TD
(P)Tj
/F26 1 Tf
7.97011 0 0 7.97011 203.64 378.36 Tm
(s)Tj
/F22 1 Tf
10.90909 0 0 10.90909 209.88 381.6 Tm
(c)Tj
/F26 1 Tf
7.97011 0 0 7.97011 214.56 379.92 Tm
(s)Tj
/F22 1 Tf
10.90909 0 0 10.90909 219 381.6 Tm
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 225.24 379.92 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 229.68 381.6 Tm
[(,)-308(then)]TJ
/F22 1 Tf
2.816 0 Td
(u)Tj
/F7 1 Tf
0.858 0 Td
[(v)55(anishes)-286(on)-286(\()]TJ
/F22 1 Tf
5.61 0 Td
(I)Tj
/F7 1 Tf
0.517 0 Td
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.21 0 Td
0.132 Tc
(\)+)Tj
/F24 1 Tf
1.43 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 378.48 385.56 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 397.32 381.6 Tm
(\))Tj
/F22 1 Tf
0.385 0 Td
(=)Tj
/F24 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 420 385.56 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 442.08 381.6 Tm
[(if)-297(and)-275(only)]TJ
-27.324 -1.243 TD
[(if)-330(for)-330(ev)33(ery)]TJ
/F22 1 Tf
5.093 0 Td
(P)Tj
/F7 1 Tf
0.781 0 Td
(\()Tj
/F22 1 Tf
(X)Tj
/F7 1 Tf
1.287 0 Td
(\))Tj
/F24 1 Tf
0.671 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(I)Tj
/F7 1 Tf
0.517 0 Td
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.199 0 Td
-0.033 Tc
[(\))-33(,)-363(we)-374(h)-33(ave)]TJ
/F30 1 Tf
1.551 -1.562 TD
0 Tc
(X)Tj
/F23 1 Tf
7.97011 0 0 7.97011 266.52 326.76 Tm
(1)Tj
/F4 1 Tf
0.52697 0 Td
<146A>Tj
/F26 1 Tf
1.12922 0 Td
(s)Tj
/F4 1 Tf
0.49686 0 Td
<6A14>Tj
/F26 1 Tf
1.12922 0 Td
(m)Tj
/F22 1 Tf
10.90909 0 0 10.90909 301.8 340.56 Tm
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 310.8 338.88 Tm
(s)Tj
/F22 1 Tf
10.90909 0 0 10.90909 315.24 340.56 Tm
(P)Tj
/F7 1 Tf
0.781 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F22 1 Tf
(c)Tj
/F26 1 Tf
7.97011 0 0 7.97011 342.6 338.88 Tm
(s)Tj
/F7 1 Tf
10.90909 0 0 10.90909 350.16 340.56 Tm
0.275 Tc
(=0)Tj
/F22 1 Tf
1.551 0 Td
0 Tc
(:)Tj
/F28 1 Tf
-20.44899 -3.201 TD
(2)Tj
/F20 1 Tf
14.34624 0 0 14.34624 144 268.92 Tm
[(3)-1130(Jet)-385(spaces)-377(in)-377(di\013eren)31(tial)-394(and)-376(di\013erence)-387(\felds)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 144 243.72 Tm
[(W)88(e)-275(study)-264(jet)-264(spaces)-275(of)-264(v)55(arieties)-286(o)33(v)33(er)-275(di\013eren)33(tial)-286(\felds)-264(and)-253(di\013erence)-275(\felds.)]TJ
0 -1.243 TD
[(W)88(e)-352(recall)-341(the)-341(concepts)-341(of)]TJ
/F22 1 Tf
11.319 0 Td
(D)Tj
/F7 1 Tf
0.858 0 Td
[({mo)-33(dules)-319(and)]TJ
/F22 1 Tf
6.358 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
[(-mo)-33(dules)-330(\(see)-352([9]\).)]TJ
/F6 1 Tf
-19.13999 -2.574 TD
[(De\fnition)-385(3.1)]TJ
/F21 1 Tf
7.337 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.804 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(D)]TJ
/F7 1 Tf
2.541 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.825 0 Td
[(b)55(e)-429(a)-440(di\013er)55(ential)-440(\feld,)-462(and)-440(let)]TJ
/F22 1 Tf
13.398 0 Td
(V)Tj
/F21 1 Tf
1.232 0 Td
[(b)55(e)-429(a)-440(\fnite-)]TJ
-27.137 -1.243 TD
(dimensional)Tj
/F22 1 Tf
5.577 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-ve)55(ctor)-374(sp)55(ac)55(e.)-495(We)-363(say)-374(that)]TJ
/F7 1 Tf
12.012 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 370.92 186.84 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 378.36 188.52 Tm
(\))Tj
/F21 1 Tf
0.759 0 Td
[(is)-363(a)]TJ
/F22 1 Tf
1.958 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
[(-mo)55(dule)-374(over)]TJ
/F22 1 Tf
5.984 0 Td
(K)Tj
/F21 1 Tf
-31.04199 -1.243 TD
(if)Tj
/F22 1 Tf
1.045 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 164.4 173.28 Tm
(V)Tj
/F21 1 Tf
10.90909 0 0 10.90909 176.4 174.96 Tm
[(is)-429(an)-429(additive)-440(endomorphism)-473(of)]TJ
/F22 1 Tf
14.498 0 Td
(V)Tj
/F21 1 Tf
1.232 0 Td
[(such)-429(that,)-462(for)-440(any)]TJ
/F22 1 Tf
8.448 0 Td
(v)Tj
/F24 1 Tf
0.924 0 Td
(2)Tj
/F22 1 Tf
1.067 0 Td
(V)Tj
/F21 1 Tf
1.232 0 Td
(and)Tj
/F22 1 Tf
-30.37099 -1.243 TD
(c)Tj
/F24 1 Tf
0.715 0 Td
(2)Tj
/F22 1 Tf
0.935 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
(,)Tj
/F22 1 Tf
0.671 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 188.4 159.72 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 195.72 161.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(cv)Tj
/F7 1 Tf
0.946 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
(cD)Tj
/F26 1 Tf
7.97011 0 0 7.97011 242.76 159.72 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 250.2 161.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
0.231 Tc
[(\)+)11(\()]TJ
/F22 1 Tf
2.002 0 Td
0.033 Tc
(Dc)Tj
/F7 1 Tf
1.287 0 Td
0 Tc
(\))Tj
/F22 1 Tf
(v)Tj
/F21 1 Tf
0.902 0 Td
(.)Tj
ET
endstream
endobj
8 0 obj
<<
/Length 18530
>>
stream
/GS4 gs
BT
/F7 1 Tf
10.90909 0 0 10.90909 144 722.16 Tm
0 g
(6)Tj
/F11 1 Tf
7.37 0 Td
[(R.)-374(Busamante)]TJ
/F12 1 Tf
5.97758 0 0 5.97758 309.72 722.16 Tm
[(R)60(ev.Mate.T)80(e)60(or.Aplic.)]TJ
/F13 1 Tf
11.4829 0 Td
((2010))Tj
/F14 1 Tf
3.7741 0 Td
(17)Tj
/F15 1 Tf
1.40525 0 Td
((1))Tj
/F6 1 Tf
10.90909 0 0 10.90909 144 686.4 Tm
[(Lemma)-385(3.2)]TJ
/F7 1 Tf
6.05 0 Td
[(\([9)-11(],)-495(3.1\))]TJ
/F21 1 Tf
4.356 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.848 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 302.64 684.72 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 310.08 686.4 Tm
(\))Tj
/F21 1 Tf
0.869 0 Td
-0.055 Tc
[(be)-528(a)]TJ
/F22 1 Tf
2.332 0 Td
0 Tc
(D)Tj
/F21 1 Tf
0.858 0 Td
[(-mo)55(dule)-484(over)-484(the)-484(di\013er)55(ential)]TJ
-19.283 -1.243 TD
(\feld)Tj
/F7 1 Tf
2.244 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(D)]TJ
/F7 1 Tf
2.541 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.781 Tc
[(.L)836(e)781(t)]TJ
/F7 1 Tf
3.311 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 257.28 671.16 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 264.72 672.84 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 268.92 676.8 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 277.8 672.84 Tm
(=)Tj
/F24 1 Tf
1.232 0 Td
(f)Tj
/F22 1 Tf
0.495 0 Td
(v)Tj
/F24 1 Tf
0.99 0 Td
(2)Tj
/F22 1 Tf
1.133 0 Td
(V)Tj
/F7 1 Tf
1.265 0 Td
(:)Tj
/F22 1 Tf
0.737 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 350.64 671.16 Tm
(V)Tj
/F22 1 Tf
10.90909 0 0 10.90909 357.96 672.84 Tm
(v)Tj
/F7 1 Tf
0.99 0 Td
0.451 Tc
(=0)Tj
/F24 1 Tf
1.727 0 Td
0 Tc
(g)Tj
/F21 1 Tf
0.968 0 Td
[(.)-759(Then)]TJ
/F7 1 Tf
3.784 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 464.4 671.16 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 471.84 672.84 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 476.04 676.8 Tm
(])Tj
/F21 1 Tf
10.90909 0 0 10.90909 484.8 672.84 Tm
(is)Tj
-31.23999 -1.243 TD
[(a)-407(\fnite-dimensional)]TJ
/F24 1 Tf
9.119 0 Td
(C)Tj
/F21 1 Tf
0.583 0 Td
[(-ve)55(ctor)-407(sp)55(ac)55(e.)-627(Mor)55(e)55(over,)-429(if)]TJ
/F7 1 Tf
12.309 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(D)]TJ
/F7 1 Tf
2.541 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.803 0 Td
[(is)-407(di\013er)55(ential)-55(ly)]TJ
-25.355 -1.243 TD
[(close)55(d,)-352(then)-352(ther)55(e)-341(is)-341(a)]TJ
/F24 1 Tf
9.779 0 Td
(C)Tj
/F21 1 Tf
0.583 0 Td
[(-b)55(asis)-341(of)]TJ
/F7 1 Tf
3.894 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 324.48 644.04 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 331.92 645.72 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 336.12 649.6801 Tm
(])Tj
/F21 1 Tf
10.90909 0 0 10.90909 343.68 645.72 Tm
[(which)-352(is)-341(a)]TJ
/F22 1 Tf
4.697 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-b)55(asis)-341(of)]TJ
/F22 1 Tf
3.894 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(.)-451(\(Thus)]TJ
-28.62199 -1.243 TD
(every)Tj
/F24 1 Tf
2.64 0 Td
(C)Tj
/F21 1 Tf
0.583 0 Td
[(-b)55(asis)-374(of)]TJ
/F7 1 Tf
3.938 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 247.08 630.48 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 254.52 632.16 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 258.72 636.12 Tm
(])Tj
/F21 1 Tf
10.90909 0 0 10.90909 266.52 632.16 Tm
[(is)-352(a)]TJ
/F22 1 Tf
1.936 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-b)55(asis)-363(of)]TJ
/F22 1 Tf
3.938 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
(\))Tj
/F6 1 Tf
-18.832 -2.376 TD
[(De\fnition)-385(3.3)]TJ
/F21 1 Tf
7.337 0 Td
(A)Tj
/F22 1 Tf
1.144 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
[(-variety)-396(is)-407(an)-396(algebr)55(aic)-418(variety)]TJ
/F22 1 Tf
13.893 0 Td
(V)Tj
/F24 1 Tf
1.155 0 Td
<12>Tj
/F25 1 Tf
1.122 0 Td
(A)Tj
/F26 1 Tf
7.97011 0 0 7.97011 430.2 610.2 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 440.16 606.2401 Tm
[(with)-407(an)-407(al-)]TJ
-27.148 -1.243 TD
[(gebr)55(aic)-374(se)55(ction)]TJ
/F22 1 Tf
6.765 0 Td
(s)Tj
/F7 1 Tf
0.781 0 Td
(:)Tj
/F22 1 Tf
0.583 0 Td
(V)Tj
/F24 1 Tf
1.111 0 Td
(!)Tj
/F22 1 Tf
1.309 0 Td
<1C>Tj
/F23 1 Tf
7.97011 0 0 7.97011 263.88 591 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 268.56 592.6801 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F21 1 Tf
0.77 0 Td
[(of)-374(the)-385(pr)55(oje)55(ction)]TJ
/F22 1 Tf
7.524 0 Td
<19>Tj
/F7 1 Tf
0.913 0 Td
(:)Tj
/F22 1 Tf
0.583 0 Td
<1C>Tj
/F23 1 Tf
7.97011 0 0 7.97011 393.12 591 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 397.8 592.6801 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F24 1 Tf
0.693 0 Td
(!)Tj
/F22 1 Tf
1.309 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(.)-506(Then,)-385(by)]TJ
-27.26899 -1.243 TD
(1.1,)Tj
/F7 1 Tf
2.002 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(s)]TJ
/F7 1 Tf
1.936 0 Td
0 Tc
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 191.16 583.08 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 198.24 579.12 Tm
(=)Tj
/F24 1 Tf
1.078 0 Td
(f)Tj
/F22 1 Tf
0.495 0 Td
(x)Tj
/F24 1 Tf
0.869 0 Td
(2)Tj
/F22 1 Tf
0.957 0 Td
(V)Tj
/F7 1 Tf
1.1 0 Td
(:)Tj
/F22 1 Tf
0.572 0 Td
0.033 Tc
(Dx)Tj
/F7 1 Tf
1.716 0 Td
0 Tc
(=)Tj
/F22 1 Tf
1.078 0 Td
(s)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
(x)Tj
/F7 1 Tf
1.43 0 Td
(\))Tj
/F24 1 Tf
(g)Tj
/F21 1 Tf
1.254 0 Td
[(is)-363(Zariski-dense)-374(in)]TJ
/F22 1 Tf
8.47 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(.)-484(We)-363(shal)-55(l)-385(write)]TJ
/F22 1 Tf
-24.79399 -1.243 TD
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 152.76 569.52 Tm
(])Tj
/F21 1 Tf
10.90909 0 0 10.90909 160.44 565.56 Tm
(when)Tj
/F22 1 Tf
2.563 0 Td
(s)Tj
/F21 1 Tf
0.825 0 Td
[(is)-352(understo)55(o)55(d.)]TJ
/F6 1 Tf
-4.895 -2.36499 TD
[(Prop)-33(osition)-396(3.4)]TJ
/F21 1 Tf
8.184 0 Td
[(A)-275(\fnite-dimensional)-286(a\016ne)-275(di\013er)55(ential)-286(algebr)55(aic)-286(variety)]TJ
-8.184 -1.243 TD
[(is)-1089(di\013er)55(ential)-55(ly)-1111(bir)55(ational)-55(ly)-1111(e)55(quivalent)-1100(to)-1089(a)-1100(set)-1089(of)-1100(the)-1089(form)]TJ
/F7 1 Tf
(\()'
/F22 1 Tf
0.055 Tc
[(V;)-110(s)]TJ
/F7 1 Tf
1.936 0 Td
0 Tc
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 169.32 516.6 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 176.28 512.64 Tm
(=)Tj
/F24 1 Tf
1.056 0 Td
(f)Tj
/F22 1 Tf
(x)Tj
/F24 1 Tf
1.342 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(V)Tj
/F7 1 Tf
1.089 0 Td
(:)Tj
/F22 1 Tf
0.55 0 Td
0.033 Tc
(Dx)Tj
/F7 1 Tf
1.705 0 Td
0 Tc
(=)Tj
/F22 1 Tf
1.056 0 Td
(s)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
(x)Tj
/F7 1 Tf
1.43 0 Td
(\))Tj
/F24 1 Tf
(g)Tj
/F21 1 Tf
1.243 0 Td
[(wher)55(e)]TJ
/F7 1 Tf
2.827 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(s)]TJ
/F7 1 Tf
1.936 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.748 0 Td
[(is)-363(a)]TJ
/F22 1 Tf
1.947 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
(-variety.)Tj
/F6 1 Tf
-21.69199 -2.376 TD
[(Remark)-385(3.5)]TJ
/F21 1 Tf
6.336 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.727 0 Td
0 Tc
(V)Tj
/F24 1 Tf
1.089 0 Td
<12>Tj
/F25 1 Tf
1.056 0 Td
(A)Tj
/F26 1 Tf
7.97011 0 0 7.97011 263.28 490.68 Tm
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 272.76 486.72 Tm
[(b)55(e)-352(a)-363(variety)-374(de\fne)55(d)-363(over)]TJ
/F22 1 Tf
11.011 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
(.)Tj
-22.561 -2.376 TD
[(1.)-506(Given)-462(a)]TJ
/F22 1 Tf
5.302 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
(-variety)Tj
/F7 1 Tf
3.795 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(s)]TJ
/F7 1 Tf
1.936 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.847 0 Td
[(,)-473(we)-462(c)55(an)-462(extend)-451(the)-462(derivation)]TJ
/F22 1 Tf
14.135 0 Td
(D)Tj
/F21 1 Tf
1.309 0 Td
[(to)-462(the)]TJ
-26.862 -1.243 TD
[(\feld)-363(of)-363(r)55(ational)-385(functions)-363(of)]TJ
/F22 1 Tf
12.562 0 Td
(V)Tj
/F21 1 Tf
1.166 0 Td
[(as)-363(fol)-55(lows:)]TJ
-13.728 -1.672 TD
(If)Tj
/F22 1 Tf
1.056 0 Td
(f)Tj
/F24 1 Tf
0.869 0 Td
0.275 Tc
(2U)Tj
/F7 1 Tf
1.672 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.199 0 Td
(\))Tj
/F21 1 Tf
[(,)-352(then)-374(we)-352(de\fne)]TJ
/F22 1 Tf
7.667 0 Td
0.033 Tc
(Df)Tj
/F7 1 Tf
1.727 0 Td
0 Tc
(=)Tj
/F30 1 Tf
1.056 0.759 TD
(P)Tj
/F26 1 Tf
7.97011 0 0 7.97011 354.72 434.04 Tm
0.06 Tc
(@f)Tj
ET
q
15.12 0 0 -0.48 352.068 431.988 cm
/Im1 Do
Q
BT
/F26 1 Tf
7.97011 0 0 7.97011 352.08 425.28 Tm
(@X)Tj
/F29 1 Tf
5.97758 0 0 5.97758 363.96 424.08 Tm
0 Tc
(i)Tj
/F22 1 Tf
10.90909 0 0 10.90909 368.4 429 Tm
(s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 373.56 427.32 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 379.32 429 Tm
(+)Tj
/F22 1 Tf
1.001 0 Td
(f)Tj
/F26 1 Tf
7.97011 0 0 7.97011 396.84 432.96 Tm
(D)Tj
/F21 1 Tf
10.90909 0 0 10.90909 404.4 429 Tm
(.)Tj
-22.693 -2.354 TD
[(2.)-506(If)]TJ
/F22 1 Tf
2.497 0 Td
(a)Tj
/F24 1 Tf
1.034 0 Td
(2)Tj
/F22 1 Tf
1.166 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 216.84 407.28 Tm
(])Tj
/F21 1 Tf
10.90909 0 0 10.90909 225.84 403.32 Tm
(and)Tj
/F22 1 Tf
2.068 0 Td
(f)Tj
/F24 1 Tf
1.1 0 Td
(2)Tj
/F27 1 Tf
1.166 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 284.52 401.64 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 297.36 403.32 Tm
0 Tc
[(,)-517(then)]TJ
/F22 1 Tf
3.168 0 Td
0.033 Tc
(Df)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
0.495 Tc
(\)=)Tj
/F30 1 Tf
3.08 0.748 TD
0 Tc
(P)Tj
/F26 1 Tf
7.97011 0 0 7.97011 398.52 408.24 Tm
0.06 Tc
(@f)Tj
ET
q
15.12 0 0 -0.48 395.988 406.308 cm
/Im1 Do
Q
BT
/F26 1 Tf
7.97011 0 0 7.97011 396 399.6 Tm
(@X)Tj
/F29 1 Tf
5.97758 0 0 5.97758 407.88 398.4 Tm
0 Tc
(i)Tj
/F22 1 Tf
10.90909 0 0 10.90909 412.2 403.32 Tm
(s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 417.36 401.64 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 420.72 403.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.319 Tc
(\)+)Tj
/F22 1 Tf
2.321 0 Td
0 Tc
(f)Tj
/F26 1 Tf
7.97011 0 0 7.97011 456.84 407.28 Tm
(D)Tj
/F7 1 Tf
10.90909 0 0 10.90909 464.4 403.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.517 Tc
(\)=)Tj
/F22 1 Tf
-27.25799 -1.441 TD
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 177.24 385.8 Tm
(f)Tj
/F7 1 Tf
10.90909 0 0 10.90909 182.76 387.6 Tm
(\()Tj
/F22 1 Tf
0.033 Tc
(Da)Tj
/F7 1 Tf
1.771 0 Td
0.297 Tc
(\)+)Tj
/F22 1 Tf
1.749 0 Td
0 Tc
(f)Tj
/F26 1 Tf
7.97011 0 0 7.97011 227.76 391.56 Tm
(D)Tj
/F7 1 Tf
10.90909 0 0 10.90909 235.44 387.6 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.451 Tc
(\)=)Tj
/F22 1 Tf
2.596 0 Td
0 Tc
(D)Tj
/F7 1 Tf
0.858 0 Td
(\()Tj
/F22 1 Tf
(f)Tj
/F7 1 Tf
0.99 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.451 Tc
[(\))451(\)=0)]TJ
/F21 1 Tf
3.476 0 Td
0 Tc
[(.)-748(Thus)]TJ
/F27 1 Tf
3.674 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 381.72 385.92 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 399.48 387.6 Tm
0 Tc
(and)Tj
/F27 1 Tf
2.035 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 433.08 392.28 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 456.96 387.6 Tm
0 Tc
[(ar)55(e)-462(dif-)]TJ
-26.191 -1.441 TD
[(fer)55(ential)-451(ide)55(als)-462(of)]TJ
/F24 1 Tf
8.107 0 Td
(O)Tj
/F26 1 Tf
7.97011 0 0 7.97011 268.32 370.2 Tm
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 281.16 371.88 Tm
0 Tc
[(,)-451(so)-451(it)-440(gives)]TJ
/F27 1 Tf
5.731 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 355.08 370.2 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 367.92 371.88 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 384.72 376.56 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 408.48 371.88 Tm
0 Tc
[(a)-440(structur)55(e)-451(of)]TJ
/F22 1 Tf
6.501 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
(-)Tj
-29.10599 -1.232 TD
[(mo)55(dule)-429(over)]TJ
/F24 1 Tf
5.72 0 Td
(U)Tj
/F21 1 Tf
0.726 0 Td
[(.)-627(De\fning)]TJ
/F22 1 Tf
5.016 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 305.64 362.28 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 314.52 358.44 Tm
(:)Tj
/F22 1 Tf
0.649 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 328.68 362.28 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 336.72 358.44 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 353.88 356.76 Tm
(a)Tj
/F24 1 Tf
10.90909 0 0 10.90909 363.12 358.44 Tm
(!)Tj
/F22 1 Tf
1.375 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 385.2 362.28 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 393.24 358.44 Tm
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.188 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 410.4 356.76 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 420 358.44 Tm
(by)Tj
/F22 1 Tf
1.353 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 444.12 362.28 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 448.92 358.44 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
0.396 Tc
(\)=)Tj
/F22 1 Tf
-27.907 -1.243 TD
0 Tc
(D)Tj
/F7 1 Tf
0.858 0 Td
(\()Tj
/F22 1 Tf
(v)Tj
/F7 1 Tf
0.902 0 Td
(\()Tj
/F22 1 Tf
(F)Tj
/F7 1 Tf
1.166 0 Td
(\)\))Tj
/F24 1 Tf
1.067 0 Td
<00>Tj
/F22 1 Tf
1.067 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F7 1 Tf
0.858 0 Td
(\()Tj
/F22 1 Tf
(F)Tj
/F7 1 Tf
1.166 0 Td
(\)\))Tj
/F21 1 Tf
1.221 0 Td
(for)Tj
/F22 1 Tf
1.683 0 Td
(v)Tj
/F24 1 Tf
0.946 0 Td
(2)Tj
/F22 1 Tf
1.089 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 319.32 348.84 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 327.36 344.88 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 344.52 343.2 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 354.36 344.88 Tm
(and)Tj
/F22 1 Tf
2.024 0 Td
(F)Tj
/F24 1 Tf
1.21 0 Td
(2)Tj
/F27 1 Tf
1.089 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 412.92 343.2 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 425.76 344.88 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 442.56 349.44 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
0.061 Tc
[(V;)61(a)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 461.4 344.88 Tm
0 Tc
[(,)-462(gives)]TJ
/F22 1 Tf
-26.598 -1.243 TD
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 178.32 335.28 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 186.36 331.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 203.64 329.64 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 212.52 331.32 Tm
[(a)-363(structur)55(e)-363(of)]TJ
/F22 1 Tf
6.259 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
[(-mo)55(dule.)]TJ
/F6 1 Tf
-13.398 -2.376 TD
[(De\fnition)-385(3.6)]TJ
/F21 1 Tf
7.337 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.738 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154<1B>]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.781 0 Td
[(b)55(e)-363(a)-374(di\013er)55(enc)55(e)-374(\feld.)-495(A)]TJ
/F22 1 Tf
10.34 0 Td
<1B>Tj
/F21 1 Tf
0.605 0 Td
[(-mo)55(dule)-374(over)]TJ
/F22 1 Tf
5.984 0 Td
(K)Tj
/F21 1 Tf
1.287 0 Td
[(is)-374(a)]TJ
-30.35999 -1.243 TD
(\fnite-dimensional)Tj
/F22 1 Tf
8.239 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-ve)55(ctor)-440(sp)55(ac)55(e)]TJ
/F22 1 Tf
6.072 0 Td
(V)Tj
/F21 1 Tf
1.243 0 Td
[(to)55(gether)-462(with)-440(an)-451(additive)-451(automor-)]TJ
-16.478 -1.243 TD
(phism)Tj
/F7 1 Tf
2.915 0 Td
0.275 Tc
<063A>Tj
/F22 1 Tf
1.551 0 Td
0 Tc
(V)Tj
/F24 1 Tf
1.089 0 Td
(!)Tj
/F22 1 Tf
1.276 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(,)-352(such)-363(that,)-374(for)-363(al)-55(l)]TJ
/F22 1 Tf
8.316 0 Td
(c)Tj
/F24 1 Tf
0.704 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(K)Tj
/F21 1 Tf
1.276 0 Td
(and)Tj
/F22 1 Tf
1.936 0 Td
(v)Tj
/F24 1 Tf
0.803 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
(,)Tj
/F7 1 Tf
0.66 0 Td
<0628>Tj
/F22 1 Tf
1.111 0 Td
(cv)Tj
/F7 1 Tf
0.946 0 Td
0.297 Tc
(\)=)Tj
/F22 1 Tf
1.738 0 Td
0 Tc
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
(c)Tj
/F7 1 Tf
<290628>Tj
/F22 1 Tf
2.31 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
(\))Tj
/F21 1 Tf
(.)Tj
/F6 1 Tf
-31.25099 -2.376 TD
[(Lemma)-385(3.7)]TJ
/F7 1 Tf
6.05 0 Td
[(\([9)-11(],)-407(4.2\))]TJ
/F21 1 Tf
4.202 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.771 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<0629>Tj
/F21 1 Tf
1.529 0 Td
-0.055 Tc
[(be)-473(a)]TJ
/F22 1 Tf
2.2 0 Td
0 Tc
<1B>Tj
/F21 1 Tf
0.605 0 Td
[(-mo)55(dule)-429(over)-407(the)-418(di\013er)55(enc)55(e)-418(\feld)]TJ
/F7 1 Tf
-17.81999 -1.243 TD
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154<1B>]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.836 Tc
[(.L)891(e)836(t)]TJ
/F7 1 Tf
3.377 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<0629>Tj
/F26 1 Tf
7.97011 0 0 7.97011 233.88 242.76 Tm
([)Tj
/F7 1 Tf
10.90909 0 0 10.90909 243.24 238.8 Tm
(=)Tj
/F24 1 Tf
1.276 0 Td
(f)Tj
/F22 1 Tf
0.495 0 Td
(v)Tj
/F24 1 Tf
1.012 0 Td
(2)Tj
/F22 1 Tf
1.166 0 Td
(V)Tj
/F7 1 Tf
1.298 0 Td
0.506 Tc
[<3A06>506(\()]TJ
/F22 1 Tf
1.892 0 Td
0 Tc
(v)Tj
/F7 1 Tf
0.517 0 Td
0.506 Tc
(\)=)Tj
/F22 1 Tf
2.156 0 Td
0 Tc
(v)Tj
/F24 1 Tf
0.517 0 Td
(g)Tj
/F21 1 Tf
[(.)-836(Then)]TJ
/F7 1 Tf
4.367 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<0629>Tj
/F26 1 Tf
7.97011 0 0 7.97011 431.64 242.76 Tm
([)Tj
/F21 1 Tf
10.90909 0 0 10.90909 440.64 238.8 Tm
[(is)-484(a)-484(\fnite-)]TJ
-27.192 -1.243 TD
(dimensional)Tj
/F22 1 Tf
5.577 0 Td
[(F)-143(ix\033)]TJ
/F21 1 Tf
2.299 0 Td
[(-ve)55(ctor)-363(sp)55(ac)55(e.)-484(Mor)55(e)55(over,)-374(if)]TJ
/F7 1 Tf
12.012 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154<1B>]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.77 0 Td
[(is)-352(a)-363(mo)55(del)-385(of)-363(A)22(CF)99(A,)]TJ
-22.94599 -1.243 TD
[(then)-352(ther)55(e)-352(is)-352(a)]TJ
/F22 1 Tf
6.6 0 Td
[(F)-143(ix\033)]TJ
/F21 1 Tf
2.299 0 Td
[(-b)55(asis)-363(of)]TJ
/F7 1 Tf
3.916 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<0629>Tj
/F26 1 Tf
7.97011 0 0 7.97011 311.88 215.64 Tm
([)Tj
/F21 1 Tf
10.90909 0 0 10.90909 319.56 211.68 Tm
[(which)-352(is)-352(a)]TJ
/F22 1 Tf
4.708 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-b)55(asis)-352(of)]TJ
/F22 1 Tf
3.916 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(.\(Thus)-352(every)]TJ
/F22 1 Tf
-26.44399 -1.232 TD
[(F)-143(ix\033)]TJ
/F21 1 Tf
2.299 0 Td
[(-b)55(asis)-363(of)]TJ
/F7 1 Tf
3.938 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<0629>Tj
/F26 1 Tf
7.97011 0 0 7.97011 240.12 202.08 Tm
([)Tj
/F21 1 Tf
10.90909 0 0 10.90909 247.92 198.24 Tm
[(is)-363(a)]TJ
/F22 1 Tf
1.947 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-b)55(asis)-352(of)]TJ
/F22 1 Tf
3.927 0 Td
(V)Tj
/F21 1 Tf
0.814 0 Td
(\))Tj
/F6 1 Tf
-17.138 -2.376 TD
[(Remark)-385(3.8)]TJ
/F21 1 Tf
6.336 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.683 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154<1B>]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.715 0 Td
[(b)55(e)-308(a)-319(mo)55(del)-330(of)-308(A)22(CF)99(A.)-297(L)55(et)]TJ
/F22 1 Tf
10.967 0 Td
0.055 Tc
[(V;)-110(W)]TJ
/F21 1 Tf
2.475 0 Td
0 Tc
[(b)55(e)-308(two)-330(irr)55(e)55(ducible)]TJ
-24.46399 -1.243 TD
[(algebr)55(aic)-484(a\016ne)-484(varieties)-484(over)]TJ
/F22 1 Tf
13.629 0 Td
(K)Tj
/F21 1 Tf
1.397 0 Td
[(such)-484(that)]TJ
/F22 1 Tf
4.554 0 Td
(W)Tj
/F24 1 Tf
1.573 0 Td
<12>Tj
/F22 1 Tf
1.276 0 Td
(V)Tj
/F24 1 Tf
1.111 0 Td
<02>Tj
/F22 1 Tf
1.089 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 421.44 162.72 Tm
<1B>Tj
/F21 1 Tf
10.90909 0 0 10.90909 427.08 158.76 Tm
[(,)-495(and)-495(assume)]TJ
ET
endstream
endobj
9 0 obj
<<
/Length 16599
>>
stream
/GS4 gs
BT
/F11 1 Tf
10.90909 0 0 10.90909 170.88 722.16 Tm
0 g
[(algebraic)-363(jet)-363(sp)66(a)22(ces)-363(and)-363(zilber)66('s)-363(dichotomy)-363(in)-385(dcf)88(a)]TJ
/F7 1 Tf
28.99599 0 Td
(7)Tj
/F21 1 Tf
-31.45999 -3.278 TD
[(that)-429(the)-418(pr)55(oje)55(ctions)-440(fr)55(om)]TJ
/F22 1 Tf
11.341 0 Td
(W)Tj
/F21 1 Tf
1.496 0 Td
(to)Tj
/F22 1 Tf
1.254 0 Td
(V)Tj
/F21 1 Tf
1.221 0 Td
(and)Tj
/F22 1 Tf
1.991 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 341.64 690.36 Tm
<1B>Tj
/F21 1 Tf
10.90909 0 0 10.90909 351.72 686.4 Tm
[(ar)55(e)-429(dominant)-429(and)-429(generic)55(al)-55(ly)]TJ
-19.041 -1.243 TD
[(\fnite-to-one.)-759(L)55(et)]TJ
/F7 1 Tf
8.217 0 Td
(\()Tj
/F22 1 Tf
[(a;)-165<1B>]TJ
/F7 1 Tf
1.958 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\)\))Tj
/F21 1 Tf
1.771 0 Td
[(b)55(e)-462(a)-462(generic)-462(p)55(oint)-473(of)]TJ
/F22 1 Tf
9.801 0 Td
(W)Tj
/F21 1 Tf
1.54 0 Td
(over)Tj
/F22 1 Tf
2.31 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(.)-759(Then,)-495(by)]TJ
-26.90599 -1.243 TD
(2.6,)Tj
/F22 1 Tf
2.002 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 172.92 663.2401 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 180.96 659.28 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(W)Tj
/F7 1 Tf
1.089 0 Td
(\))Tj
/F23 1 Tf
7.97011 0 0 7.97011 201.24 657 Tm
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 235.32 659.28 Tm
[(induc)55(es)-374(an)-363(isomorphism)]TJ
/F22 1 Tf
10.89 0 Td
(f)Tj
/F21 1 Tf
0.968 0 Td
(of)Tj
/F22 1 Tf
1.177 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-ve)55(ctor)-363(sp)55(ac)55(es)-385(b)55(etwe)55(en)]TJ
/F22 1 Tf
-22.33 -1.243 TD
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 151.08 649.6801 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 159.12 645.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 176.28 644.04 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 184.8 645.72 Tm
(and)Tj
/F22 1 Tf
1.892 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 212.52 649.6801 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 220.56 645.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 237.72 643.44 Tm
<1B>Tj
/F23 1 Tf
0.63236 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 254.52 645.72 Tm
[(.)-440(We)-308(have)-319(also)-330(that)]TJ
/F7 1 Tf
8.778 0 Td
(\()Tj
/F22 1 Tf
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 361.56 649.6801 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 369.6 645.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 386.76 644.04 Tm
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 391.8 645.72 Tm
0.165 Tc
(;f)Tj
/F4 1 Tf
7.97011 0 0 7.97011 403.2 649.6801 Tm
0 Tc
<00>Tj
/F23 1 Tf
0.8281 0 Td
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 414.48 645.72 Tm
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\))Tj
/F21 1 Tf
0.704 0 Td
[(is)-308(a)]TJ
/F22 1 Tf
1.848 0 Td
<1B>Tj
/F21 1 Tf
0.605 0 Td
[(-mo)55(dule)]TJ
-28.55599 -1.243 TD
(over)Tj
/F22 1 Tf
2.211 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
(.)Tj
/F20 1 Tf
14.34624 0 0 14.34624 144 597.6 Tm
[(4)-1130(Jet)-385(spaces)-377(in)-377(di\013erence-di\013eren)28(tial)-402(\felds)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 144 573.2401 Tm
[(W)88(e)-539(describ)-33(e)-517(the)-528(jet)-539(spaces)-528(of)-528(\fnite-dimensional)-528(v)55(arieties)-550(de\fned)-506(o)33(v)33(er)]TJ
0 -1.243 TD
[(di\013erence-di\013eren)33(tial)-374(\felds,)-352(and)-341(w)33(e)-363(state)-363(the)-352(results)-352(needed)-352(to)-352(pro)33(v)33(e)-363(our)]TJ
T*
[(main)-396(theorem)-407(4.8.)-649(Finally)-407(w)33(e)-396(giv)33(e)-418(t)33(w)33(o)-407(corollaries:)-594(the)-407(\frst)-385(is)-396(the)-407(w)33(eak)]TJ
T*
[(dic)33(hotom)33(y)88(,)-484(and)-429(the)-429(second)-440(is)-429(an)-429(application)-451(to)-440(quan)33(ti\fer-free)-440(de\fnable)]TJ
(groups.)'
1.551 -1.243 TD
[(W)88(e)-352(start)-341(with)-330(the)-330(de\fnition)-330(of)-341(a)-341(\()]TJ
/F22 1 Tf
-0.022 Tc
[<1B3B>-187(D)]TJ
/F7 1 Tf
16.775 0 Td
0 Tc
[(\)-mo)-33(dule.)]TJ
/F6 1 Tf
-18.326 -2.354 TD
[(De\fnition)-385(4.1)]TJ
/F21 1 Tf
7.337 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.76 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.165 Tc
[(K)154<3B1B>187(;D)]TJ
/F7 1 Tf
3.531 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.803 0 Td
[(b)55(e)-385(a)-396(di\013er)55(enc)55(e-di\013er)55(ential)-407(\feld.)-572(A)]TJ
/F7 1 Tf
15.543 0 Td
(\()Tj
/F22 1 Tf
-0.022 Tc
[<1B3B>-187(D)]TJ
/F7 1 Tf
2.233 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.385 0 Td
(-)Tj
-31.59199 -1.243 TD
[(mo)55(dule)-495(over)]TJ
/F22 1 Tf
5.852 0 Td
(K)Tj
/F21 1 Tf
1.397 0 Td
[(is)-473(a)-484(\fnite-dimensional)]TJ
/F22 1 Tf
10.45 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-ve)55(ctor)-484(sp)55(ac)55(e)]TJ
/F22 1 Tf
6.16 0 Td
(V)Tj
/F21 1 Tf
1.287 0 Td
[(e)55(quipp)55(e)55(d)-495(with)]TJ
-26.07 -1.243 TD
[(an)-484(additive)-484(automorphism)]TJ
/F7 1 Tf
12.089 0 Td
0.484 Tc
<063A>Tj
/F22 1 Tf
1.98 0 Td
0 Tc
(V)Tj
/F24 1 Tf
1.298 0 Td
(!)Tj
/F22 1 Tf
1.485 0 Td
(V)Tj
/F21 1 Tf
1.276 0 Td
[(and)-484(an)-484(additive)-484(endomorphism)]TJ
/F22 1 Tf
-18.128 -1.243 TD
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 153 437.4 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 164.88 439.08 Tm
(:)Tj
/F22 1 Tf
0.704 0 Td
(V)Tj
/F24 1 Tf
1.232 0 Td
(!)Tj
/F22 1 Tf
1.419 0 Td
(V)Tj
/F21 1 Tf
0.803 0 Td
[(,)-451(such)-440(that)]TJ
/F7 1 Tf
5.236 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(D)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 292.32 437.4 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 299.76 439.08 Tm
(\))Tj
/F21 1 Tf
0.836 0 Td
[(is)-429(a)]TJ
/F22 1 Tf
2.09 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
[(-mo)55(dule)-451(over)]TJ
/F22 1 Tf
6.127 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
(,)Tj
/F7 1 Tf
0.759 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<0629>Tj
/F21 1 Tf
1.562 0 Td
[(is)-440(a)]TJ
/F22 1 Tf
2.101 0 Td
<1B>Tj
/F21 1 Tf
0.605 0 Td
(-)Tj
-31.60299 -1.243 TD
[(mo)55(dule)-374(over)]TJ
/F22 1 Tf
5.61 0 Td
(K)Tj
/F21 1 Tf
1.276 0 Td
[(and)-374(for)-363(al)-55(l)]TJ
/F22 1 Tf
4.972 0 Td
(v)Tj
/F24 1 Tf
0.803 0 Td
(2)Tj
/F22 1 Tf
0.935 0 Td
(V)Tj
/F21 1 Tf
1.166 0 Td
[(we)-363(have)]TJ
/F7 1 Tf
3.784 0 Td
<0628>Tj
/F22 1 Tf
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 367.44 423.84 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 374.76 425.52 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
[(\)\))-297(=)]TJ
/F22 1 Tf
2.123 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 416.76 423.84 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 424.08 425.52 Tm
<280628>Tj
/F22 1 Tf
(v)Tj
/F7 1 Tf
2.013 0 Td
(\)\))Tj
/F21 1 Tf
0.77 0 Td
(.)Tj
/F7 1 Tf
-26.90599 -2.354 TD
[(The)-330(k)33(ey)-341(p)-33(oin)33(t)-341(of)-330(our)-330(pro)-33(of)-330(of)-330(4.8)-352(is)-330(the)-341(follo)33(wing)-341(lemma.)]TJ
/F6 1 Tf
-1.551 -2.354 TD
[(Lemma)-385(4.2)]TJ
/F21 1 Tf
6.05 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.617 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<06>Tj
/F22 1 Tf
0.165 Tc
(;D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 265.32 372.48 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 272.76 374.16 Tm
(\))Tj
/F21 1 Tf
0.649 0 Td
-0.055 Tc
[(be)-308(a)]TJ
/F7 1 Tf
1.892 0 Td
0 Tc
(\()Tj
/F22 1 Tf
-0.022 Tc
[<1B3B>-187(D)]TJ
/F7 1 Tf
2.233 0 Td
0 Tc
(\))Tj
/F21 1 Tf
[(-mo)55(dule)-275(over)-264(the)-264(di\013er)55(enc)55(e-di\013er)55(en-)]TJ
-16.577 -1.243 TD
[(tial)-319(\feld)]TJ
/F7 1 Tf
3.806 0 Td
(\()Tj
/F22 1 Tf
0.165 Tc
[(K)154<3B1B>187(;D)]TJ
/F7 1 Tf
3.531 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.462 Tc
[(.L)517(e)462(t)]TJ
/F7 1 Tf
2.827 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.055 Tc
(V;)Tj
/F7 1 Tf
1.463 0 Td
0 Tc
<06>Tj
/F22 1 Tf
0.165 Tc
(;D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 292.56 358.92 Tm
0 Tc
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 300 360.6 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 304.2 364.56 Tm
(\\)Tj
/F7 1 Tf
10.90909 0 0 10.90909 311.16 360.6 Tm
(=)Tj
/F24 1 Tf
1.056 0 Td
(f)Tj
/F22 1 Tf
0.495 0 Td
(v)Tj
/F24 1 Tf
0.803 0 Td
(2)Tj
/F22 1 Tf
0.935 0 Td
(V)Tj
/F7 1 Tf
1.089 0 Td
(:)Tj
/F22 1 Tf
0.55 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 373.92 358.92 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 381.36 360.6 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
0.286 Tc
[(\)=)11(0)]TJ
/F24 1 Tf
2.332 0 Td
0 Tc
(^)Tj
/F7 1 Tf
0.781 0 Td
<0628>Tj
/F22 1 Tf
1.111 0 Td
(v)Tj
/F7 1 Tf
0.517 0 Td
0.275 Tc
(\)=)Tj
/F22 1 Tf
1.716 0 Td
0 Tc
(v)Tj
/F24 1 Tf
0.517 0 Td
(g)Tj
/F7 1 Tf
0.814 0 Td
(\()Tj
/F21 1 Tf
(we)Tj
-30.44799 -1.243 TD
[(shal)-55(l)-330(write)]TJ
/F22 1 Tf
4.807 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 205.32 351 Tm
(\\)Tj
/F21 1 Tf
10.90909 0 0 10.90909 212.52 347.04 Tm
(when)Tj
/F22 1 Tf
2.508 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 248.88 345.36 Tm
(V)Tj
/F21 1 Tf
10.90909 0 0 10.90909 259.68 347.04 Tm
(and)Tj
/F7 1 Tf
1.903 0 Td
<06>Tj
/F21 1 Tf
1.034 0 Td
[(ar)55(e)-330(understo)55(o)55(d)]TJ
/F7 1 Tf
6.391 0 Td
(\))Tj
/F21 1 Tf
[(.)-484(Then)]TJ
/F22 1 Tf
3.751 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 411.12 351 Tm
(\\)Tj
/F21 1 Tf
10.90909 0 0 10.90909 418.32 347.04 Tm
[(is)-319(a)]TJ
/F7 1 Tf
1.859 0 Td
(\()Tj
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.827 0 Td
0.132 Tc
(\\C)Tj
/F7 1 Tf
1.386 0 Td
0 Tc
(\))Tj
/F21 1 Tf
(-)Tj
-31.21799 -1.243 TD
[(ve)55(ctor)-550(sp)55(ac)55(e.)-1001(Mor)55(e)55(over,)-594(if)]TJ
/F7 1 Tf
12.76 0 Td
(\()Tj
/F22 1 Tf
0.165 Tc
[(K)154<3B1B>187(;D)]TJ
/F7 1 Tf
3.531 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.935 0 Td
[(is)-539(a)-539(mo)55(del)-561(of)-539(DCF)99(A,)-528(ther)55(e)-539(is)-539(a)]TJ
/F7 1 Tf
-17.22599 -1.243 TD
(\()Tj
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.893 0 Td
0.198 Tc
(\\C)Tj
/F7 1 Tf
1.452 0 Td
0 Tc
(\))Tj
/F21 1 Tf
[(-b)55(asis)-363(of)]TJ
/F22 1 Tf
4.312 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 247.2 323.88 Tm
(\\)Tj
/F21 1 Tf
10.90909 0 0 10.90909 254.88 319.92 Tm
[(which)-352(is)-352(a)]TJ
/F22 1 Tf
4.719 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-b)55(asis)-352(of)]TJ
/F22 1 Tf
3.916 0 Td
(V)Tj
/F21 1 Tf
0.814 0 Td
[(.)-451(\(Thus)-352(every)]TJ
/F7 1 Tf
6.325 0 Td
(\()Tj
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F7 1 Tf
2.684 0 Td
(\))Tj
/F24 1 Tf
0.605 0 Td
0.198 Tc
(\\C)Tj
/F21 1 Tf
1.452 0 Td
0 Tc
(-)Tj
-31.60299 -1.232 TD
[(b)55(asis)-363(of)]TJ
/F7 1 Tf
3.575 0 Td
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.199 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 200.28 310.44 Tm
(\\)Tj
/F21 1 Tf
10.90909 0 0 10.90909 207.96 306.48 Tm
[(is)-363(a)]TJ
/F22 1 Tf
1.947 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(-b)55(asis)-352(of)]TJ
/F22 1 Tf
3.927 0 Td
(V)Tj
/F21 1 Tf
0.814 0 Td
(\))Tj
/F11 1 Tf
-13.47499 -2.354 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
[(It)-385(is)-385(clear)-396(that)]TJ
/F22 1 Tf
6.842 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 244.44 271.2 Tm
(\\)Tj
/F7 1 Tf
10.90909 0 0 10.90909 252.36 267.24 Tm
0.385 Tc
[(i)385(sa\()]TJ
/F22 1 Tf
2.321 0 Td
0 Tc
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.563 0 Td
0.253 Tc
(\\C)Tj
/F7 1 Tf
1.507 0 Td
0 Tc
[(\)-v)33(ector)-407(space.)-605(By)-385(3.2)-396(and)-374(3.7)-396(it)-385(is)]TJ
-16.32399 -1.243 TD
[(enough)-341(to)-352(pro)33(v)33(e)-341(that)-352(there)-341(is)-341(a)-352(\()]TJ
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
16.896 0 Td
0.22 Tc
(\\C)Tj
/F7 1 Tf
1.474 0 Td
0 Tc
[(\)-basis)-352(of)]TJ
/F22 1 Tf
4.334 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 400.44 257.64 Tm
(\\)Tj
/F7 1 Tf
10.90909 0 0 10.90909 408 253.68 Tm
[(whic)33(h)-341(is)-341(a)]TJ
/F24 1 Tf
4.719 0 Td
(C)Tj
/F7 1 Tf
0.583 0 Td
(-basis)Tj
-29.502 -1.243 TD
(of)Tj
/F22 1 Tf
1.144 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 165.24 244.08 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 168.96 240.12 Tm
(.)Tj
-0.737 -1.243 TD
(Let)Tj
/F24 1 Tf
1.87 0 Td
(f)Tj
/F22 1 Tf
(v)Tj
/F23 1 Tf
7.97011 0 0 7.97011 192 224.88 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 196.8 226.56 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
(;v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 228.12 224.76 Tm
0 Tc
(k)Tj
/F24 1 Tf
10.90909 0 0 10.90909 233.28 226.56 Tm
(g)Tj
/F7 1 Tf
0.924 0 Td
0.033 Tc
[(be)-374(a)]TJ
/F24 1 Tf
2.354 0 Td
0 Tc
(C)Tj
/F7 1 Tf
0.583 0 Td
[(-basis)-418(of)]TJ
/F22 1 Tf
4.092 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 328.8 230.52 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 332.64 226.56 Tm
[(,)-440(then)]TJ
/F24 1 Tf
3.069 0 Td
(f)Tj
/F7 1 Tf
0.495 0 Td
<0628>Tj
/F22 1 Tf
1.111 0 Td
(v)Tj
/F23 1 Tf
7.97011 0 0 7.97011 388.92 224.88 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 393.72 226.56 Tm
(\))Tj
/F22 1 Tf
0.385 0 Td
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
0 Tc
(;)Tj
/F7 1 Tf
0.44 0 Td
<0628>Tj
/F22 1 Tf
1.111 0 Td
(v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 441.36 224.76 Tm
(k)Tj
/F7 1 Tf
10.90909 0 0 10.90909 446.52 226.56 Tm
(\))Tj
/F24 1 Tf
0.385 0 Td
(g)Tj
/F7 1 Tf
0.924 0 Td
[(is)-418(a)]TJ
/F24 1 Tf
2.002 0 Td
(C)Tj
/F7 1 Tf
0.583 0 Td
(-)Tj
-31.62499 -1.243 TD
[(basis)-693(of)]TJ
/F22 1 Tf
4.323 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 199.92 216.96 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 203.64 213 Tm
[(.)-1540(Let)]TJ
/F22 1 Tf
3.971 0 Td
(A)Tj
/F7 1 Tf
1.441 0 Td
[(b)-33(e)-693(the)-693(in)33(v)33(ertible)]TJ
/F22 1 Tf
8.591 0 Td
(k)Tj
/F24 1 Tf
1.012 0 Td
<02>Tj
/F22 1 Tf
1.243 0 Td
(k)Tj
/F24 1 Tf
1.254 0 Td
(C)Tj
/F7 1 Tf
0.583 0 Td
[(-matrix)-704(suc)33(h)-693(that)]TJ
-23.56199 -1.243 TD
<5B0628>Tj
/F22 1 Tf
1.386 0 Td
(v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 164.4 197.76 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 167.88 199.44 Tm
(\)])Tj
/F26 1 Tf
7.97011 0 0 7.97011 175.08 203.4 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 181.68 199.44 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
(A)Tj
/F7 1 Tf
0.748 0 Td
([)Tj
/F22 1 Tf
(v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 209.64 197.76 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 213.12 199.44 Tm
(])Tj
/F26 1 Tf
7.97011 0 0 7.97011 216.12 203.4 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 219.72 199.44 Tm
(.)Tj
-5.39 -1.243 TD
(Let)Tj
/F24 1 Tf
1.716 0 Td
(f)Tj
/F22 1 Tf
0.495 0 Td
(u)Tj
/F23 1 Tf
7.97011 0 0 7.97011 191.28 184.2 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 196.08 185.88 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
(;u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 228.36 184.08 Tm
0 Tc
(k)Tj
/F24 1 Tf
10.90909 0 0 10.90909 233.52 185.88 Tm
(g)Tj
/F7 1 Tf
0.759 0 Td
0.033 Tc
[(be)-209(a)]TJ
/F24 1 Tf
2.035 0 Td
0 Tc
(C)Tj
/F7 1 Tf
0.583 0 Td
[(-basis)-264(of)]TJ
/F22 1 Tf
3.773 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 320.4 189.84 Tm
(])Tj
/F7 1 Tf
10.90909 0 0 10.90909 324.12 185.88 Tm
[(.)-418(Then)-253(there)-253(exists)-264(an)-264(in)33(v)33(ertible)]TJ
/F22 1 Tf
14.047 0 Td
(k)Tj
/F24 1 Tf
0.616 0 Td
<02>Tj
/F22 1 Tf
-31.17399 -1.243 TD
(k)Tj
/F24 1 Tf
1.452 0 Td
(C)Tj
/F7 1 Tf
0.583 0 Td
(-matrix)Tj
/F22 1 Tf
4.147 0 Td
(B)Tj
/F7 1 Tf
1.705 0 Td
[(suc)33(h)-891(that)-902([)]TJ
/F22 1 Tf
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 299.76 170.64 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 303.12 172.32 Tm
(])Tj
/F26 1 Tf
7.97011 0 0 7.97011 306.12 176.28 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 322.92 172.32 Tm
(=)Tj
/F22 1 Tf
1.991 0 Td
(B)Tj
/F7 1 Tf
0.814 0 Td
([)Tj
/F22 1 Tf
0.275 0 Td
(v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 361.8 170.64 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 365.16 172.32 Tm
(])Tj
/F26 1 Tf
7.97011 0 0 7.97011 368.16 176.28 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 371.76 172.32 Tm
[(;)-1177(applying)-891<06>-891(w)33(e)-902(get)]TJ
-20.878 -1.243 TD
<5B0628>Tj
/F22 1 Tf
1.386 0 Td
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 165.36 157.08 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 168.72 158.76 Tm
(\)])Tj
/F26 1 Tf
7.97011 0 0 7.97011 175.92 162.72 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 183.6 158.76 Tm
(=)Tj
/F22 1 Tf
1.144 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(B)Tj
/F7 1 Tf
0.814 0 Td
<295B0628>Tj
/F22 1 Tf
1.771 0 Td
(v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 240.36 157.08 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 243.84 158.76 Tm
(\)])Tj
/F26 1 Tf
7.97011 0 0 7.97011 251.04 162.72 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 258.6 158.76 Tm
(=)Tj
/F22 1 Tf
1.144 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(B)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F22 1 Tf
(A)Tj
/F7 1 Tf
1.133 0 Td
([)Tj
/F22 1 Tf
(v)Tj
/F26 1 Tf
7.97011 0 0 7.97011 311.4 157.08 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 314.88 158.76 Tm
(])Tj
/F26 1 Tf
7.97011 0 0 7.97011 317.88 162.72 Tm
(t)Tj
/F7 1 Tf
10.90909 0 0 10.90909 321.48 158.76 Tm
[(.)-605(Th)33(us)]TJ
/F24 1 Tf
3.476 0 Td
(f)Tj
/F22 1 Tf
0.495 0 Td
(u)Tj
/F23 1 Tf
7.97011 0 0 7.97011 371.04 157.08 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 375.72 158.76 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
(;u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 408 156.96 Tm
0 Tc
(k)Tj
/F24 1 Tf
10.90909 0 0 10.90909 413.16 158.76 Tm
(g)Tj
/F7 1 Tf
0.891 0 Td
[(is)-385(in)]TJ
/F22 1 Tf
2.277 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 456.48 162.72 Tm
(\\)Tj
/F7 1 Tf
10.90909 0 0 10.90909 464.52 158.76 Tm
[(if)-385(and)]TJ
ET
endstream
endobj
10 0 obj
<<
/Length 26657
>>
stream
/GS4 gs
BT
/F7 1 Tf
10.90909 0 0 10.90909 144 722.16 Tm
0 g
(8)Tj
/F11 1 Tf
7.37 0 Td
[(R.)-374(Busamante)]TJ
/F12 1 Tf
5.97758 0 0 5.97758 309.72 722.16 Tm
[(R)60(ev.Mate.T)80(e)60(or.Aplic.)]TJ
/F13 1 Tf
11.4829 0 Td
((2010))Tj
/F14 1 Tf
3.7741 0 Td
(17)Tj
/F15 1 Tf
1.40525 0 Td
((1))Tj
/F7 1 Tf
10.90909 0 0 10.90909 144 686.4 Tm
[(only)-451(if)]TJ
/F22 1 Tf
3.344 0 Td
(B)Tj
/F7 1 Tf
1.287 0 Td
(=)Tj
/F22 1 Tf
1.254 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(B)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F22 1 Tf
(A)Tj
/F7 1 Tf
[(.)-814(Since)-451(\()]TJ
/F24 1 Tf
(C)Tj
/F22 1 Tf
5.918 0 Td
0.165 Tc
<3B1B>Tj
/F7 1 Tf
1.045 0 Td
0 Tc
(\))Tj
/F24 1 Tf
0.88 0 Td
(j)Tj
/F7 1 Tf
0.11 0 Td
(=)Tj
/F22 1 Tf
1.254 0 Td
[(AC)-77(F)-143(A)]TJ
/F7 1 Tf
[(,)-484(the)-462(system)]TJ
/F22 1 Tf
9.108 0 Td
(X)Tj
/F7 1 Tf
1.386 0 Td
(=)Tj
/F22 1 Tf
1.254 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
(X)Tj
/F7 1 Tf
1.287 0 Td
(\))Tj
/F22 1 Tf
(A)Tj
/F7 1 Tf
1.133 0 Td
(,)Tj
-31.66899 -1.243 TD
(where)Tj
/F22 1 Tf
2.981 0 Td
(X)Tj
/F7 1 Tf
1.331 0 Td
[(is)-429(an)-418(in)33(v)33(ertible)]TJ
/F22 1 Tf
7.084 0 Td
(k)Tj
/F24 1 Tf
0.836 0 Td
<02>Tj
/F22 1 Tf
1.056 0 Td
(k)Tj
/F7 1 Tf
0.979 0 Td
[(matrix,)-451(has)-429(a)-429(solution)-429(in)]TJ
/F24 1 Tf
11.572 0 Td
(C)Tj
/F7 1 Tf
0.583 0 Td
[(.)-726(So)-418(w)33(e)-429(can)]TJ
-26.422 -1.243 TD
[(supp)-33(ose)-319(that)]TJ
/F24 1 Tf
5.929 0 Td
(f)Tj
/F22 1 Tf
(u)Tj
/F23 1 Tf
7.97011 0 0 7.97011 220.32 657.6 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 225.12 659.28 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
(;u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 257.4 657.48 Tm
0 Tc
(k)Tj
/F24 1 Tf
10.90909 0 0 10.90909 262.56 659.28 Tm
(g)Tj
/F7 1 Tf
0.825 0 Td
[(is)-341(in)]TJ
/F22 1 Tf
2.178 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 304.08 663.2401 Tm
(\\)Tj
/F7 1 Tf
10.90909 0 0 10.90909 307.92 659.28 Tm
(.)Tj
-13.475 -1.276 TD
(Let)Tj
/F22 1 Tf
1.87 0 Td
(v)Tj
/F24 1 Tf
0.913 0 Td
(2)Tj
/F22 1 Tf
1.067 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 211.68 649.32 Tm
(\\)Tj
/F7 1 Tf
10.90909 0 0 10.90909 215.52 645.36 Tm
[(,)-429(and)-396(let)]TJ
/F22 1 Tf
4.235 0 Td
<15>Tj
/F23 1 Tf
7.97011 0 0 7.97011 268.08 643.6801 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 272.88 645.36 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.331 0 Td
0 Tc
<15>Tj
/F26 1 Tf
7.97011 0 0 7.97011 298.56 643.56 Tm
(k)Tj
/F24 1 Tf
10.90909 0 0 10.90909 308.04 645.36 Tm
0.396 Tc
(2C)Tj
/F7 1 Tf
2.057 0 Td
0 Tc
[(suc)33(h)-407(that)]TJ
/F22 1 Tf
4.565 0 Td
(v)Tj
/F7 1 Tf
0.924 0 Td
(=)Tj
/F22 1 Tf
1.177 0 Td
<15>Tj
/F23 1 Tf
7.97011 0 0 7.97011 409.56 643.6801 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 414.24 645.36 Tm
(u)Tj
/F23 1 Tf
7.97011 0 0 7.97011 420.48 643.6801 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 428.28 645.36 Tm
(+)Tj
/F24 1 Tf
1.045 0 Td
0.165 Tc
<010101>Tj
/F7 1 Tf
1.441 0 Td
0 Tc
(+)Tj
/F22 1 Tf
1.045 0 Td
<15>Tj
/F26 1 Tf
7.97011 0 0 7.97011 473.16 643.56 Tm
(k)Tj
/F22 1 Tf
10.90909 0 0 10.90909 478.32 645.36 Tm
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 484.56 643.56 Tm
(k)Tj
/F7 1 Tf
10.90909 0 0 10.90909 489.6 645.36 Tm
(.)Tj
-31.67999 -1.243 TD
(Then)Tj
/F22 1 Tf
2.563 0 Td
(v)Tj
/F7 1 Tf
0.803 0 Td
(=)Tj
/F22 1 Tf
1.056 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
<15>Tj
/F23 1 Tf
7.97011 0 0 7.97011 209.4 630.12 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 214.2 631.8 Tm
(\))Tj
/F22 1 Tf
(u)Tj
/F23 1 Tf
7.97011 0 0 7.97011 224.64 630.12 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 230.88 631.8 Tm
(+)Tj
/F24 1 Tf
0.913 0 Td
0.165 Tc
<010101>Tj
/F7 1 Tf
1.298 0 Td
0 Tc
(+)Tj
/F22 1 Tf
0.913 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
<15>Tj
/F26 1 Tf
7.97011 0 0 7.97011 282.12 630 Tm
(k)Tj
/F7 1 Tf
10.90909 0 0 10.90909 287.28 631.8 Tm
(\))Tj
/F22 1 Tf
0.385 0 Td
(u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 297.72 630 Tm
(k)Tj
/F7 1 Tf
10.90909 0 0 10.90909 302.88 631.8 Tm
[(,)-308(th)33(us)]TJ
/F22 1 Tf
2.739 0 Td
<15>Tj
/F26 1 Tf
7.97011 0 0 7.97011 339.12 630.12 Tm
(i)Tj
/F24 1 Tf
10.90909 0 0 10.90909 345.48 631.8 Tm
(2)Tj
/F22 1 Tf
0.946 0 Td
[(F)-143(ix\033)]TJ
/F7 1 Tf
2.596 0 Td
(for)Tj
/F22 1 Tf
1.485 0 Td
(i)Tj
/F7 1 Tf
0.627 0 Td
0.264 Tc
(=1)Tj
/F22 1 Tf
1.54 0 Td
0 Tc
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.518 0 Td
(;k)Tj
/F7 1 Tf
0.99 0 Td
0 Tc
[(.)-440(Hence)]TJ
/F24 1 Tf
-28.61099 -1.24299 TD
(f)Tj
/F22 1 Tf
0.495 0 Td
(u)Tj
/F23 1 Tf
7.97011 0 0 7.97011 155.64 616.56 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 160.44 618.2401 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.507 0 Td
(;u)Tj
/F26 1 Tf
7.97011 0 0 7.97011 192.72 616.44 Tm
0 Tc
(k)Tj
/F24 1 Tf
10.90909 0 0 10.90909 197.88 618.2401 Tm
(g)Tj
/F7 1 Tf
0.836 0 Td
[(is)-330(a)-341(\()]TJ
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
4.752 0 Td
0.22 Tc
(\\C)Tj
/F7 1 Tf
1.474 0 Td
0 Tc
[(\)-basis)-341(of)]TJ
/F22 1 Tf
4.312 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 330.72 622.2 Tm
(\\)Tj
/F22 1 Tf
10.90909 0 0 10.90909 334.56 618.2401 Tm
(:)Tj
/F28 1 Tf
0.616 0 Td
(2)Tj
/F6 1 Tf
-18.084 -2.563 TD
[(Notation)-374(4.3)]TJ
/F21 1 Tf
6.82 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
2.222 0 Td
0 Tc
(\()Tj
/F24 1 Tf
(U)Tj
/F22 1 Tf
1.111 0 Td
0.165 Tc
[<3B1B>187(;D)]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
1.265 0 Td
[(b)55(e)-869(a)-869(satur)55(ate)55(d)-891(mo)55(del)-880(of)-869(DCF)99(A.)-858(L)55(et)]TJ
/F22 1 Tf
-13.706 -1.24299 TD
(K)Tj
/F7 1 Tf
1.452 0 Td
(=)Tj
/F22 1 Tf
1.298 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\))Tj
/F21 1 Tf
0.891 0 Td
[(b)55(e)-495(a)-495(di\013er)55(enc)55(e-di\013er)55(ential)-506(sub\feld)-506(of)]TJ
/F24 1 Tf
17.061 0 Td
(U)Tj
/F21 1 Tf
0.726 0 Td
[(,)-528(and)-506(let)]TJ
/F22 1 Tf
4.455 0 Td
(a)Tj
/F24 1 Tf
1.056 0 Td
0.528 Tc
(2U)Tj
/F26 1 Tf
7.97011 0 0 7.97011 487.08 580.68 Tm
0 Tc
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 144 563.16 Tm
[(such)-363(that)]TJ
/F22 1 Tf
4.323 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 215.4 561.48 Tm
(D)Tj
/F7 1 Tf
10.90909 0 0 10.90909 226.08 563.16 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F21 1 Tf
0.748 0 Td
(and)Tj
/F22 1 Tf
1.947 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F24 1 Tf
1.199 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 345.48 567.12 Tm
[(al)-15(g)]TJ
/F21 1 Tf
10.90909 0 0 10.90909 357.48 563.16 Tm
(.)Tj
-18.018 -1.276 TD
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.672 0 Td
0 Tc
(V)Tj
/F21 1 Tf
1.111 0 Td
[(b)55(e)-308(the)-308(lo)55(cus)-308(of)]TJ
/F22 1 Tf
6.325 0 Td
(a)Tj
/F21 1 Tf
0.836 0 Td
(over)Tj
/F22 1 Tf
2.156 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(,)-308(and)-308(let)]TJ
/F22 1 Tf
3.85 0 Td
(W)Tj
/F21 1 Tf
1.386 0 Td
[(b)55(e)-308(the)-308(lo)55(cus)-308(of)]TJ
/F7 1 Tf
6.325 0 Td
(\()Tj
/F22 1 Tf
[(a;)-165<1B>]TJ
/F7 1 Tf
1.958 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\)\))Tj
/F21 1 Tf
2.013 0 Td
(over)Tj
/F22 1 Tf
-30.10699 -1.243 TD
(K)Tj
/F21 1 Tf
0.924 0 Td
[(.)-440(Then)]TJ
/F22 1 Tf
3.289 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 198.84 539.64 Tm
<1B>Tj
/F21 1 Tf
10.90909 0 0 10.90909 207.72 535.68 Tm
[(is)-297(the)-308(lo)55(cus)-308(of)]TJ
/F22 1 Tf
6.16 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F21 1 Tf
1.221 0 Td
(over)Tj
/F22 1 Tf
2.156 0 Td
(K)Tj
/F21 1 Tf
1.221 0 Td
[(and)-308(the)-308(pr)55(oje)55(ctions)]TJ
/F22 1 Tf
8.481 0 Td
<19>Tj
/F23 1 Tf
7.97011 0 0 7.97011 434.64 534 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 442.32 535.68 Tm
(:)Tj
/F22 1 Tf
0.561 0 Td
(W)Tj
/F24 1 Tf
1.364 0 Td
-0.176 Tc
<0021>Tj
/F22 1 Tf
1.881 0 Td
0 Tc
(V)Tj
/F21 1 Tf
-31.15199 -1.243 TD
(and)Tj
/F22 1 Tf
1.947 0 Td
<19>Tj
/F23 1 Tf
7.97011 0 0 7.97011 171.48 520.44 Tm
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 179.16 522.12 Tm
(:)Tj
/F22 1 Tf
0.561 0 Td
(W)Tj
/F24 1 Tf
1.353 0 Td
-0.165 Tc
<0021>Tj
/F22 1 Tf
1.892 0 Td
0 Tc
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 229.44 526.08 Tm
<1B>Tj
/F21 1 Tf
10.90909 0 0 10.90909 239.04 522.12 Tm
[(ar)55(e)-363(generic)55(al)-55(ly)-363(\fnite-to-one)-363(and)-374(dominant.)]TJ
-7.161 -1.276 TD
[(We)-352(set:)]TJ
/F22 1 Tf
0 -1.27599 TD
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 167.52 498.24 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 175.32 494.28 Tm
(:)Tj
/F22 1 Tf
0.55 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
0.275 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(])Tj
/F24 1 Tf
0.55 0 Td
-0.165 Tc
<0021>Tj
/F22 1 Tf
1.892 0 Td
0 Tc
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
(W)Tj
/F7 1 Tf
1.364 0 Td
(])Tj
/F21 1 Tf
0.275 0 Td
(,)Tj
/F22 1 Tf
0.66 0 Td
(F)Tj
/F24 1 Tf
1.056 0 Td
[<3700>165(!)]TJ
/F22 1 Tf
1.892 0 Td
(F)Tj
/F24 1 Tf
1.001 0 Td
<0E>Tj
/F22 1 Tf
0.726 0 Td
<19>Tj
/F23 1 Tf
7.97011 0 0 7.97011 322.32 492.6 Tm
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 327 494.28 Tm
(.)Tj
/F22 1 Tf
-15.224 -1.287 TD
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 167.52 484.2 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 175.32 480.24 Tm
(:)Tj
/F22 1 Tf
0.55 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
0.275 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 203.28 484.2 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 208.8 480.24 Tm
(])Tj
/F24 1 Tf
0.561 0 Td
-0.165 Tc
<0021>Tj
/F22 1 Tf
1.892 0 Td
0 Tc
(K)Tj
/F7 1 Tf
0.924 0 Td
([)Tj
/F22 1 Tf
0.275 0 Td
(W)Tj
/F7 1 Tf
1.089 0 Td
(])Tj
/F21 1 Tf
(,)Tj
/F22 1 Tf
0.935 0 Td
(G)Tj
/F24 1 Tf
1.067 0 Td
[<3700>176(!)]TJ
/F22 1 Tf
1.881 0 Td
(G)Tj
/F24 1 Tf
1.012 0 Td
<0E>Tj
/F22 1 Tf
0.726 0 Td
<19>Tj
/F23 1 Tf
7.97011 0 0 7.97011 328.08 478.56 Tm
(2)Tj
/F21 1 Tf
10.90909 0 0 10.90909 332.76 480.24 Tm
(.)Tj
ET
q
11.4 0 0 -0.48 160.908 475.548 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 160.92 466.32 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 167.52 470.16 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 175.32 466.32 Tm
(:)Tj
/F27 1 Tf
0.55 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 192.72 464.64 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 205.56 466.32 Tm
0 Tc
(=)Tj
/F27 1 Tf
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 222.36 470.88 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -0.99371 TD
0.061 Tc
[(V;)61(a)]TJ
/F24 1 Tf
10.90909 0 0 10.90909 244.32 466.32 Tm
-0.176 Tc
<0021>Tj
/F27 1 Tf
1.892 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 276.36 464.16 Tm
-0.03 Tc
(W;)Tj
/F23 1 Tf
1.27978 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F22 1 Tf
10.90909 0 0 10.90909 316.56 466.32 Tm
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 333.36 470.88 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.06899 TD
-0.03 Tc
(W;)Tj
/F23 1 Tf
1.27978 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 377.64 466.32 Tm
[(the)-363(map)-374(induc)55(e)55(d)-374(by)]TJ
/F22 1 Tf
8.767 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 479.88 470.28 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
ET
q
11.4 0 0 -0.48 160.908 458.508 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 160.92 449.28 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 167.52 453 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 176.04 449.28 Tm
(:)Tj
/F27 1 Tf
0.627 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 194.28 447 Tm
(V)Tj
/F29 1 Tf
5.97758 0 0 5.97758 201.12 449.28 Tm
<1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 206.16 447 Tm
<3B1B>Tj
/F23 1 Tf
0.93349 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F22 1 Tf
10.90909 0 0 10.90909 225.24 449.28 Tm
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 242.04 453.84 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
(V)Tj
/F29 1 Tf
5.97758 0 0 5.97758 249 448.08 Tm
<1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 253.92 445.8 Tm
(;a)Tj
/F24 1 Tf
10.90909 0 0 10.90909 265.08 449.28 Tm
-0.165 Tc
<0021>Tj
/F27 1 Tf
1.958 0 Td
0 Tc
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 297.84 447 Tm
-0.03 Tc
(W;)Tj
/F23 1 Tf
1.27978 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F22 1 Tf
10.90909 0 0 10.90909 338.16 449.28 Tm
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 354.96 453.84 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.06899 TD
-0.03 Tc
(W;)Tj
/F23 1 Tf
1.27978 0 Td
0 Tc
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 399.72 449.28 Tm
[(the)-396(map)-407(induc)55(e)55(d)-418(by)]TJ
/F22 1 Tf
-23.441 -1.342 TD
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 150.6 438.6 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F22 1 Tf
10.90909 0 0 10.90909 160.92 420.72 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 167.52 424.68 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 174.96 420.72 Tm
(:)Tj
/F22 1 Tf
0.55 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 188.04 424.68 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 196.08 420.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(W)Tj
/F7 1 Tf
1.089 0 Td
(\))Tj
/F23 1 Tf
7.97011 0 0 7.97011 216.36 418.44 Tm
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F24 1 Tf
10.90909 0 0 10.90909 249.6 420.72 Tm
-0.176 Tc
<0021>Tj
/F22 1 Tf
1.881 0 Td
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 277.2 424.68 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 285.24 420.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 302.52 419.04 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 307.56 420.72 Tm
(,)Tj
/F22 1 Tf
0.66 0 Td
(w)Tj
/F24 1 Tf
1.023 0 Td
[<3700>176(!)]TJ
/F22 1 Tf
1.881 0 Td
(w)Tj
/F24 1 Tf
0.968 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 364.908 429.948 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 364.92 420.72 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 371.52 424.44 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 376.2 420.72 Tm
(.)Tj
/F22 1 Tf
-19.734 -1.397 TD
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 167.52 409.44 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 174.96 405.48 Tm
(:)Tj
/F22 1 Tf
0.55 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 188.04 409.44 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 196.08 405.48 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(W)Tj
/F7 1 Tf
1.089 0 Td
(\))Tj
/F23 1 Tf
7.97011 0 0 7.97011 216.36 403.2 Tm
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F24 1 Tf
10.90909 0 0 10.90909 249.6 405.48 Tm
-0.176 Tc
<0021>Tj
/F22 1 Tf
1.881 0 Td
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 277.2 409.44 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 285.24 405.48 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 298.32 409.44 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 303.84 405.48 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 308.04 403.2 Tm
<1B>Tj
/F23 1 Tf
0.63236 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 324.84 405.48 Tm
(,)Tj
/F22 1 Tf
0.66 0 Td
(w)Tj
/F24 1 Tf
1.023 0 Td
[<3700>165(!)]TJ
/F22 1 Tf
1.892 0 Td
(w)Tj
/F24 1 Tf
0.968 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 382.188 414.708 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 382.2 405.48 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 388.8 409.2 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F21 1 Tf
10.90909 0 0 10.90909 393.6 405.48 Tm
(.)Tj
-22.88 -1.243 TD
[(With)-484(r)55(esp)55(e)55(ct)-506(to)-484(the)-495(extension)-495(of)]TJ
/F22 1 Tf
14.982 0 Td
(D)Tj
/F21 1 Tf
1.342 0 Td
[(to)-484(the)-495(c)55(o)55(or)55(dinate)-517(rings,)]TJ
/F22 1 Tf
11.011 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 448.8 395.88 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 458.76 391.92 Tm
(and)Tj
/F22 1 Tf
2.068 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 487.92 395.88 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(2)Tj
/F21 1 Tf
10.90909 0 0 10.90909 144 378.36 Tm
[(ar)55(e)-429(di\013er)55(ential)-418(homomorphisms.)-682(By)-407(2.6)]TJ
/F22 1 Tf
18.205 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 349.2 382.32 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 357.96 378.36 Tm
(and)Tj
/F22 1 Tf
2.002 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 386.4 382.32 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(2)Tj
/F21 1 Tf
10.90909 0 0 10.90909 395.28 378.36 Tm
[(ar)55(e)-418(isomorphisms)-451(of)]TJ
/F24 1 Tf
-23.034 -1.243 TD
(U)Tj
/F21 1 Tf
0.726 0 Td
[(-ve)55(ctor)-363(sp)55(ac)55(es.)]TJ
0.825 -1.276 TD
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.892 0 Td
0 Tc
(f)Tj
/F7 1 Tf
1.155 0 Td
(:)Tj
/F22 1 Tf
0.847 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 210.48 354.84 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 218.52 350.88 Tm
(\()Tj
/F22 1 Tf
(V)Tj
/F7 1 Tf
1.188 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 235.68 349.2 Tm
(a)Tj
/F24 1 Tf
10.90909 0 0 10.90909 246.96 350.88 Tm
-0.176 Tc
<0021>Tj
/F22 1 Tf
2.178 0 Td
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 277.8 354.84 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 285.72 350.88 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 298.8 354.84 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 304.44 350.88 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 308.64 348.6 Tm
<1B>Tj
/F23 1 Tf
0.63236 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F21 1 Tf
10.90909 0 0 10.90909 331.08 350.88 Tm
[(b)55(e)-517(the)]TJ
/F24 1 Tf
3.201 0 Td
(U)Tj
/F21 1 Tf
0.726 0 Td
[(-isomorphism)-539(de\fne)55(d)-539(by)]TJ
/F22 1 Tf
-21.076 -1.243 TD
(f)Tj
/F7 1 Tf
0.88 0 Td
(=)Tj
/F22 1 Tf
1.056 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 171.72 341.28 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(2)Tj
/F24 1 Tf
10.90909 0 0 10.90909 178.44 337.32 Tm
<0E>Tj
/F7 1 Tf
0.726 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 197.16 341.28 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 201.48 337.32 Tm
(\))Tj
/F4 1 Tf
7.97011 0 0 7.97011 205.68 341.28 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 217.08 337.32 Tm
(.)Tj
-5.148 -1.276 TD
[(Sinc)55(e)]TJ
/F22 1 Tf
2.805 0 Td
0.033 Tc
(Da)Tj
/F24 1 Tf
1.936 0 Td
0 Tc
(2)Tj
/F22 1 Tf
1.221 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F21 1 Tf
1.43 0 Td
[(ther)55(e)-517(is)-506(a)-517(r)55(ational)-528(map)]TJ
/F22 1 Tf
11.099 0 Td
(s)Tj
/F7 1 Tf
1.012 0 Td
(:)Tj
/F22 1 Tf
0.836 0 Td
(V)Tj
/F24 1 Tf
1.353 0 Td
0.55 Tc
(!U)Tj
/F26 1 Tf
7.97011 0 0 7.97011 436.68 327.36 Tm
0 Tc
(n)Tj
/F21 1 Tf
10.90909 0 0 10.90909 447.84 323.4 Tm
[(such)-506(that)]TJ
/F22 1 Tf
-27.852 -1.243 TD
(s)Tj
/F7 1 Tf
0.473 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.638 Tc
(\)=)Tj
/F22 1 Tf
2.959 0 Td
0.033 Tc
(Da)Tj
/F21 1 Tf
1.936 0 Td
0 Tc
(and)Tj
/F7 1 Tf
2.134 0 Td
(\()Tj
/F22 1 Tf
0.055 Tc
[(V;)-110(s)]TJ
/F7 1 Tf
1.936 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.946 0 Td
[(is)-561(a)]TJ
/F22 1 Tf
2.332 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
[(-variety.)-1045(By)-561(c)55(onstruction)]TJ
/F7 1 Tf
12.342 0 Td
(\()Tj
/F22 1 Tf
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 443.88 313.8 Tm
<1B>Tj
/F22 1 Tf
10.90909 0 0 10.90909 449.52 309.84 Tm
0.165 Tc
(;s)Tj
/F26 1 Tf
7.97011 0 0 7.97011 459.48 313.8 Tm
0 Tc
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 465.12 309.84 Tm
(\))Tj
/F21 1 Tf
0.935 0 Td
(and)Tj
/F7 1 Tf
-30.37099 -1.243 TD
(\()Tj
/F22 1 Tf
-0.033 Tc
(W;)Tj
/F7 1 Tf
1.738 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(s;)-165(s)]TJ
/F26 1 Tf
7.97011 0 0 7.97011 182.28 300.24 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 188.04 296.28 Tm
(\)\))Tj
/F21 1 Tf
1.133 0 Td
[(ar)55(e)-374(also)]TJ
/F22 1 Tf
3.751 0 Td
(D)Tj
/F21 1 Tf
0.858 0 Td
(-varieties.)Tj
/F6 1 Tf
-9.779 -2.53 TD
[(Lemma)-385(4.4)]TJ
/F7 1 Tf
6.05 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 221.28 272.64 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 229.32 268.68 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 246.48 267 Tm
(a)Tj
/F22 1 Tf
10.90909 0 0 10.90909 251.52 268.68 Tm
0.165 Tc
(;f)Tj
/F4 1 Tf
7.97011 0 0 7.97011 262.92 272.64 Tm
0 Tc
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 274.2 268.68 Tm
-0.022 Tc
[<1B3B>-187(D)]TJ
/F4 1 Tf
7.97011 0 0 7.97011 294.36 272.64 Tm
0 Tc
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 299.16 268.68 Tm
(\))Tj
/F21 1 Tf
0.748 0 Td
[(is)-363(a)]TJ
/F7 1 Tf
1.947 0 Td
(\()Tj
/F22 1 Tf
-0.022 Tc
[<1B3B>-187(D)]TJ
/F7 1 Tf
2.233 0 Td
0 Tc
(\))Tj
/F21 1 Tf
[(-mo)55(dule.)]TJ
/F11 1 Tf
-19.15099 -2.519 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.276 TD
[(All)-649(w)33(e)-649(need)-649(to)-649(pro)33(v)33(e)-649(is)-649(that)]TJ
/F22 1 Tf
14.707 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 330.72 231.24 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 342.48 227.28 Tm
[(comm)33(utes)-649(with)]TJ
/F22 1 Tf
7.59 0 Td
(f)Tj
/F4 1 Tf
7.97011 0 0 7.97011 431.88 231.24 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 443.16 227.28 Tm
<1B>Tj
/F7 1 Tf
0.605 0 Td
[(.)-1375(Since)]TJ
/F22 1 Tf
-28.02799 -1.243 TD
(f)Tj
/F7 1 Tf
0.88 0 Td
(=)Tj
/F22 1 Tf
1.056 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 171.72 217.68 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F24 1 Tf
10.90909 0 0 10.90909 178.56 213.72 Tm
<0E>Tj
/F7 1 Tf
0.726 0 Td
(\()Tj
/F22 1 Tf
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 197.28 217.68 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 201.6 213.72 Tm
(\))Tj
/F4 1 Tf
7.97011 0 0 7.97011 205.8 217.68 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 220.8 213.72 Tm
(and)Tj
/F22 1 Tf
1.947 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 248.64 217.68 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 253.08 213.72 Tm
0.165 Tc
<3B19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 264.48 217.68 Tm
0 Tc
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 272.52 213.72 Tm
[(are)-341(isomorphisms,)-330(and)-330(since)]TJ
/F22 1 Tf
12.595 0 Td
<1B>Tj
/F7 1 Tf
0.935 0 Td
[(comm)33(utes)-352(with)]TJ
/F22 1 Tf
-25.31099 -1.243 TD
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 153.36 204.12 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 158.04 200.16 Tm
[(,)-341(it)-341(is)-330(enough)-330(to)-341(pro)33(v)33(e)-352(that)]TJ
/F22 1 Tf
12.155 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 300 204.12 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 308.28 200.16 Tm
[(comm)33(utes)-341(with)]TJ
/F22 1 Tf
6.974 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 390.96 204.12 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 399 200.16 Tm
(and)Tj
/F22 1 Tf
1.947 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 426.84 204.12 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 431.16 200.16 Tm
(.)Tj
-24.772 -1.276 TD
(Let)Tj
/F22 1 Tf
1.793 0 Td
(w)Tj
/F24 1 Tf
1.023 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 209.04 190.2 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 216.96 186.24 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(W)Tj
/F7 1 Tf
1.089 0 Td
(\))Tj
/F23 1 Tf
7.97011 0 0 7.97011 237.24 183.96 Tm
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a;\033)Tj
/F23 1 Tf
1.49057 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\)\))Tj
/F7 1 Tf
10.90909 0 0 10.90909 271.08 186.24 Tm
(and)Tj
/F22 1 Tf
1.947 0 Td
(F)Tj
/F24 1 Tf
1.056 0 Td
(2)Tj
/F27 1 Tf
0.946 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 325.56 184.56 Tm
0.061 Tc
[(V;)61(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 338.4 186.24 Tm
0 Tc
(=)Tj
/F27 1 Tf
0.495 0 Td
(M)Tj
/F26 1 Tf
7.97011 0 0 7.97011 355.2 190.8 Tm
(m)Tj
/F23 1 Tf
0.93349 0 Td
(+1)Tj
/F26 1 Tf
-0.93349 -1.00877 TD
0.061 Tc
[(V;)61(a)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 374.04 186.24 Tm
0 Tc
(.)Tj
-19.536 -1.276 TD
[(W)88(e)-429(w)33(an)33(t)-429(to)-429(pro)33(v)33(e)-429(that)]TJ
/F22 1 Tf
10.681 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 286.8 176.28 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 291.48 172.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 302.28 176.28 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 306.72 172.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F7 1 Tf
0.737 0 Td
(\)\)\()Tj
/F22 1 Tf
1.155 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
0.44 Tc
[(\)=)22(\()]TJ
/F22 1 Tf
2.409 0 Td
0 Tc
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 372.96 176.28 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F24 1 Tf
10.90909 0 0 10.90909 380.4 172.32 Tm
<0E>Tj
/F22 1 Tf
0.781 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 398.28 176.28 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 402.96 172.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F7 1 Tf
0.737 0 Td
(\)\)\()Tj
/F22 1 Tf
1.155 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
[(\).)-726(W)88(e)-429(ha)33(v)33(e)]TJ
/F22 1 Tf
-26.79599 -1.243 TD
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 153.36 162.72 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 158.04 158.76 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 168.84 162.72 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 173.28 158.76 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F7 1 Tf
0.737 0 Td
(\)\)\()Tj
/F22 1 Tf
1.155 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
0.297 Tc
(\)=)Tj
/F22 1 Tf
1.738 0 Td
0 Tc
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 234.96 162.72 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 239.76 158.76 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F24 1 Tf
0.968 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 262.308 167.988 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 262.32 158.76 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 268.92 162.48 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 273.72 158.76 Tm
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
(D)Tj
/F7 1 Tf
0.858 0 Td
(\(\()Tj
/F22 1 Tf
0.77 0 Td
(w)Tj
/F24 1 Tf
0.979 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 345.708 167.988 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 345.72 158.76 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 352.32 162.48 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 357.12 158.76 Tm
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
(\)\))Tj
/F24 1 Tf
1.001 0 Td
<00>Tj
/F22 1 Tf
1.001 0 Td
(w)Tj
/F24 1 Tf
0.968 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 414.348 167.988 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 414.36 158.76 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 420.96 162.48 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 425.64 158.76 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F7 1 Tf
0.858 0 Td
(\()Tj
/F22 1 Tf
(F)Tj
/F7 1 Tf
1.166 0 Td
(\)\).)Tj
ET
endstream
endobj
11 0 obj
<<
/Length 21423
>>
stream
/GS4 gs
BT
/F11 1 Tf
10.90909 0 0 10.90909 170.88 722.16 Tm
0 g
[(algebraic)-363(jet)-363(sp)66(a)22(ces)-363(and)-363(zilber)66('s)-363(dichotomy)-363(in)-385(dcf)88(a)]TJ
/F7 1 Tf
28.99599 0 Td
(9)Tj
-29.90899 -3.278 TD
[(On)-242(the)-264(other)-253(hand)]TJ
/F22 1 Tf
8.184 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 256.8 690.36 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 261.12 686.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 274.68 690.36 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 279.48 686.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F7 1 Tf
0.737 0 Td
(\)\)\()Tj
/F22 1 Tf
1.155 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
0.308 Tc
[(\)=)33(\()]TJ
/F22 1 Tf
2.134 0 Td
0 Tc
(D)Tj
/F4 1 Tf
7.97011 0 0 7.97011 345.48 690.36 Tm
<03>Tj
/F7 1 Tf
10.90909 0 0 10.90909 350.16 686.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F7 1 Tf
0.737 0 Td
(\))Tj
/F24 1 Tf
0.451 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 373.428 695.628 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 373.44 686.4 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 380.04 690.1201 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 384.96 686.4 Tm
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
(D)Tj
/F7 1 Tf
0.858 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(w)Tj
/F7 1 Tf
0.737 0 Td
(\()Tj
ET
q
11.4 0 0 -0.48 446.508 695.628 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 446.52 686.4 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 453.12 690.1201 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 458.04 686.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
(\)\)\))Tj
/F24 1 Tf
1.221 0 Td
<00>Tj
/F22 1 Tf
-31.17399 -1.243 TD
(w)Tj
/F7 1 Tf
0.737 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 165.24 671.16 Tm
(W)Tj
/F7 1 Tf
10.90909 0 0 10.90909 175.08 672.84 Tm
(\()Tj
ET
q
11.4 0 0 -0.48 179.268 682.068 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 179.28 672.84 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 185.88 676.56 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 190.68 672.84 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
(\)\).)Tj
-3.894 -1.243 TD
[(But)-473(clearly)]TJ
/F22 1 Tf
5.445 0 Td
(D)Tj
/F7 1 Tf
0.858 0 Td
(\(\()Tj
/F22 1 Tf
0.77 0 Td
(w)Tj
/F24 1 Tf
1.067 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 258.468 668.508 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 258.48 659.28 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 265.08 663 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 269.88 659.28 Tm
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
[(\)\))-517(=)]TJ
/F22 1 Tf
2.563 0 Td
(D)Tj
/F7 1 Tf
0.858 0 Td
(\()Tj
/F22 1 Tf
(w)Tj
/F7 1 Tf
1.122 0 Td
(\()Tj
ET
q
11.4 0 0 -0.48 340.548 668.508 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 340.56 659.28 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 347.16 663 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 351.96 659.28 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
[(\)\)\))-484(and)]TJ
/F22 1 Tf
3.718 0 Td
(w)Tj
/F24 1 Tf
1.056 0 Td
<0E>Tj
ET
q
11.4 0 0 -0.48 425.508 668.508 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 425.52 659.28 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 432.12 663 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 436.92 659.28 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 450.12 657.6 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 457.44 659.28 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
[(\)\))-517(=)]TJ
/F22 1 Tf
-29.89799 -1.243 TD
(w)Tj
/F7 1 Tf
0.737 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 165.24 644.04 Tm
(V)Tj
/F7 1 Tf
10.90909 0 0 10.90909 172.68 645.72 Tm
(\()Tj
ET
q
11.4 0 0 -0.48 176.868 654.948 cm
/Im1 Do
Q
BT
/F22 1 Tf
10.90909 0 0 10.90909 176.88 645.72 Tm
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 183.48 649.44 Tm
<03>Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 188.28 645.72 Tm
(\)\()Tj
/F22 1 Tf
0.77 0 Td
(F)Tj
/F7 1 Tf
0.781 0 Td
(\)\).)Tj
-5.61 -1.243 TD
[(The)-330(pro)-33(of)-319(is)-341(similar)-341(for)]TJ
/F22 1 Tf
10.494 0 Td
<19>Tj
/F4 1 Tf
7.97011 0 0 7.97011 265.08 636.12 Tm
(0)Tj
/F23 1 Tf
-0.04517 -0.85821 TD
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 269.4 632.16 Tm
(.)Tj
/F28 1 Tf
0.726 0 Td
(2)Tj
/F6 1 Tf
-12.221 -2.277 TD
[(Lemma)-385(4.5)]TJ
/F21 1 Tf
6.05 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.705 0 Td
0 Tc
(K)Tj
/F24 1 Tf
1.199 0 Td
<12>Tj
/F22 1 Tf
1.056 0 Td
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 262.44 605.64 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 270.24 607.32 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 309.12 605.64 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 313.92 607.32 Tm
(\))Tj
/F21 1 Tf
0.451 Tc
[(.L)506(e)451(t)]TJ
/F22 1 Tf
2.86 0 Td
0 Tc
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 351.48 605.64 Tm
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 359.88 607.32 Tm
[(b)55(e)-341(the)]TJ
/F7 1 Tf
2.849 0 Td
(\()Tj
/F22 1 Tf
-0.022 Tc
[<1B3B>-187(D)]TJ
/F7 1 Tf
2.233 0 Td
0 Tc
(\))Tj
/F21 1 Tf
[(-lo)55(cus)-352(of)]TJ
/F22 1 Tf
4.367 0 Td
(a)Tj
/F21 1 Tf
0.869 0 Td
(over)Tj
/F22 1 Tf
-30.10699 -1.24299 TD
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 153.24 592.08 Tm
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 158.04 593.76 Tm
[(,)-341(and)-341(let)]TJ
/F22 1 Tf
3.949 0 Td
(c)Tj
/F21 1 Tf
0.77 0 Td
[(b)55(e)-341(the)-341(\feld)-352(of)-341(de\fnition)-341(of)]TJ
/F22 1 Tf
11.748 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 344.04 592.08 Tm
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 348.72 593.76 Tm
[(.)-451(Then)]TJ
/F22 1 Tf
3.344 0 Td
(c)Tj
/F24 1 Tf
0.715 0 Td
<12>Tj
/F22 1 Tf
1.056 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a=K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 468 592.08 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 472.68 593.76 Tm
(\)\))Tj
/F24 1 Tf
1.056 0 Td
<12>Tj
/F22 1 Tf
-31.18499 -1.243 TD
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(c)]TJ
/F7 1 Tf
2.112 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.385 0 Td
(.)Tj
/F11 1 Tf
-3.773 -2.27699 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
(Clearly)Tj
/F22 1 Tf
3.52 0 Td
(c)Tj
/F24 1 Tf
0.781 0 Td
<12>Tj
/F22 1 Tf
1.133 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a=K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 283.68 540.12 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 288.36 541.8 Tm
[(\)\).)-583(W)88(e)-385(kno)33(w)-385(that)]TJ
/F22 1 Tf
8.25 0 Td
(a)Tj
/F24 1 Tf
0.869 0.198 TD
(j)Tj
/F22 1 Tf
-0.352 -0.341 TD
(^)Tj
/F26 1 Tf
7.97011 0 0 7.97011 394.92 539.76 Tm
0.015 Tc
[(K;)15(c)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 408.72 541.8 Tm
0 Tc
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 417.96 540.12 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 426.84 541.8 Tm
(in)Tj
/F21 1 Tf
1.21 0 Td
(DCF)Tj
/F7 1 Tf
2.497 0 Td
[(,)-374(also)]TJ
/F22 1 Tf
-29.63399 -1.375 TD
<1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 150.6 530.76 Tm
(i)Tj
/F7 1 Tf
10.90909 0 0 10.90909 153.96 526.8 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(D)Tj
/F26 1 Tf
7.97011 0 0 7.97011 167.52 530.76 Tm
(j)Tj
/F22 1 Tf
10.90909 0 0 10.90909 171.96 526.8 Tm
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F24 1 Tf
1.826 0 Td
<12>Tj
/F22 1 Tf
2.211 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 246 530.76 Tm
[(al)-15(g)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 257.88 526.8 Tm
[(;)-1375(then)]TJ
/F22 1 Tf
4.62 0 Td
(acl)Tj
/F26 1 Tf
7.97011 0 0 7.97011 321.96 525.12 Tm
-0.03 Tc
[<1B3B>-30(D)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 336.72 526.8 Tm
0 Tc
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(a)]TJ
/F7 1 Tf
2.211 0 Td
0 Tc
(\))Tj
/F24 1 Tf
0.748 0.198 TD
(j)Tj
/F22 1 Tf
-0.352 -0.352 TD
(^)Tj
/F26 1 Tf
7.97011 0 0 7.97011 376.08 524.64 Tm
0.015 Tc
[(K;)15(c)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 389.88 526.8 Tm
0 Tc
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 399.12 525.12 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 415.08 526.8 Tm
(in)Tj
/F21 1 Tf
1.859 0 Td
-0.022 Tc
[(AC)-22(F)]TJ
/F7 1 Tf
2.09 0 Td
0 Tc
[(,)-1023(th)33(us)]TJ
/F22 1 Tf
-28.79799 -1.243 TD
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a=K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 207.48 511.56 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 212.16 513.24 Tm
(\)\))Tj
/F24 1 Tf
1.056 0 Td
<12>Tj
/F22 1 Tf
1.056 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(c)]TJ
/F7 1 Tf
2.112 0 Td
0 Tc
(\))Tj
/F22 1 Tf
0.385 0 Td
(:)Tj
/F28 1 Tf
0.638 0 Td
(2)Tj
/F6 1 Tf
-12.771 -2.277 TD
[(Remark)-385(4.6)]TJ
/F21 1 Tf
6.336 0 Td
[(If)-352(we)-352(r)55(eplac)55(e)]TJ
/F22 1 Tf
5.841 0 Td
(a)Tj
/F21 1 Tf
0.88 0 Td
(by)Tj
/F7 1 Tf
1.287 0 Td
(\()Tj
/F22 1 Tf
[(a;)-165<1B>]TJ
/F7 1 Tf
1.958 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F22 1 Tf
(;)Tj
/F24 1 Tf
1.738 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.529 0 Td
<3B1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 368.88 492.36 Tm
0 Tc
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 376.92 488.4 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\)\))Tj
/F21 1 Tf
1.133 0 Td
(for)Tj
/F22 1 Tf
1.584 0 Td
(m)Tj
/F21 1 Tf
1.232 0 Td
[(lar)55(ge)-352(enough,)]TJ
/F22 1 Tf
-26.213 -1.243 TD
(c)Tj
/F21 1 Tf
0.847 0 Td
(and)Tj
/F22 1 Tf
2.002 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.385 0 Td
(a=K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 238.56 473.16 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 243.24 474.84 Tm
(\)\))Tj
/F21 1 Tf
1.188 0 Td
[(wil)-55(l)-418(b)55(e)-418(inter)55(de\fnable)-429(over)]TJ
/F22 1 Tf
11.726 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
[(\(cho)55(ose)]TJ
/F22 1 Tf
3.63 0 Td
(m)Tj
/F21 1 Tf
1.287 0 Td
[(for)-418(which)]TJ
-27.85199 -1.243 TD
[(the)-363(Morley)-352(r)55(ank)-374(of)]TJ
/F22 1 Tf
8.47 0 Td
(tp)Tj
/F26 1 Tf
7.97011 0 0 7.97011 245.88 459.6 Tm
0.03 Tc
[(DC)-45(F)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 266.64 461.28 Tm
0 Tc
(\()Tj
/F22 1 Tf
0.385 0 Td
<1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 277.44 465.24 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 285.6 461.28 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F22 1 Tf
0.385 0 Td
(=K)Tj
/F7 1 Tf
1.419 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a;)Tj
/F24 1 Tf
0.968 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.518 0 Td
<3B1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 357.96 465.24 Tm
0 Tc
(m)Tj
/F4 1 Tf
0.93349 0 Td
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 376.8 461.28 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\)\)\))Tj
/F21 1 Tf
1.529 0 Td
[(is)-352(minimal)-374(and)-363(for)]TJ
-23.78199 -1.243 TD
[(which)-308(the)-308(Morley)-297(de)55(gr)55(e)55(e)-308(of)]TJ
/F22 1 Tf
11.715 0 Td
(tp)Tj
/F26 1 Tf
7.97011 0 0 7.97011 281.28 446.04 Tm
0.03 Tc
[(DC)-45(F)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 302.04 447.72 Tm
0 Tc
(\()Tj
/F22 1 Tf
0.385 0 Td
<1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 312.84 451.68 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 320.88 447.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F22 1 Tf
0.385 0 Td
(=K)Tj
/F7 1 Tf
1.419 0 Td
(\()Tj
/F22 1 Tf
(a;)Tj
/F24 1 Tf
1.353 0 Td
0.165 Tc
<010101>Tj
/F22 1 Tf
1.518 0 Td
<3B1B>Tj
/F26 1 Tf
7.97011 0 0 7.97011 393.24 451.68 Tm
0 Tc
(m)Tj
/F4 1 Tf
0.93349 0 Td
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 412.08 447.72 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\)\)\))Tj
/F21 1 Tf
1.474 0 Td
[(is)-297(minimal\))]TJ
-26.96099 -1.243 TD
(.)Tj
/F6 1 Tf
0 -2.277 TD
[(Lemma)-385(4.7)]TJ
/F21 1 Tf
6.05 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.771 0 Td
0 Tc
(K)Tj
/F24 1 Tf
1.276 0 Td
<12>Tj
/F22 1 Tf
1.144 0 Td
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 264.96 407.64 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 273.6 409.32 Tm
(=)Tj
/F22 1 Tf
1.144 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 313.44 407.64 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 318.24 409.32 Tm
(\))Tj
/F21 1 Tf
0.605 Tc
[(.L)660(e)605(t)]TJ
/F22 1 Tf
3.069 0 Td
0 Tc
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 358.08 407.64 Tm
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 367.2 409.32 Tm
[(b)55(e)-396(the)-418(lo)55(cus)-407(of)]TJ
/F22 1 Tf
6.721 0 Td
(a)Tj
/F21 1 Tf
0.935 0 Td
(over)Tj
/F22 1 Tf
2.255 0 Td
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 484.56 407.64 Tm
(1)Tj
/F21 1 Tf
10.90909 0 0 10.90909 489.36 409.32 Tm
(.)Tj
-31.658 -1.232 TD
(Then)Tj
/F22 1 Tf
2.607 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 179.52 399.84 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 187.56 395.88 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 198.12 394.2 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 202.92 395.88 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 207.12 394.2 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 216 395.88 Tm
[(is)-363(a)]TJ
/F7 1 Tf
1.947 0 Td
(\()Tj
/F22 1 Tf
-0.022 Tc
[<1B3B>-187(D)]TJ
/F7 1 Tf
2.233 0 Td
0 Tc
(\))Tj
/F21 1 Tf
[(-submo)55(dule)-374(of)]TJ
/F22 1 Tf
6.732 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 342.12 399.84 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 350.16 395.88 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 367.32 394.2 Tm
(a)Tj
/F21 1 Tf
10.90909 0 0 10.90909 372.36 395.88 Tm
(.)Tj
/F11 1 Tf
-20.933 -2.277 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
(Clearly)Tj
/F22 1 Tf
3.597 0 Td
(J)Tj
/F7 1 Tf
0.649 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 217.8 355.8 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 222.6 357.48 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 226.8 355.8 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 236.76 357.48 Tm
[(is)-462(a)]TJ
/F22 1 Tf
2.079 0 Td
(D)Tj
/F7 1 Tf
0.858 0 Td
[(-submo)-33(dule)-440(of)]TJ
/F22 1 Tf
6.743 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 349.44 361.44 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 357.48 357.48 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 374.76 355.8 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 379.8 357.48 Tm
[(.)-803(Let)]TJ
/F22 1 Tf
2.992 0 Td
(W)Tj
/F23 1 Tf
7.97011 0 0 7.97011 422.76 355.8 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 432.36 357.48 Tm
[(b)-33(e)-451(the)-462(lo)-33(cus)]TJ
-26.43299 -1.243 TD
[(of)-429(\()]TJ
/F22 1 Tf
[(a;)-165<1B>]TJ
/F7 1 Tf
3.19 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
[(\)\))-462(o)33(v)33(er)]TJ
/F22 1 Tf
3.993 0 Td
(K)Tj
/F23 1 Tf
7.97011 0 0 7.97011 235.8 342.24 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 240.6 343.92 Tm
[(.)-737(Let)]TJ
/F22 1 Tf
2.893 0 Td
(f)Tj
/F23 1 Tf
7.97011 0 0 7.97011 277.56 342.24 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 286.92 343.92 Tm
[(b)-33(e)-429(the)-429(isomorphism)-429(b)-33(et)33(w)33(een)]TJ
/F22 1 Tf
13.178 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 437.76 347.88 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 445.8 343.92 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 456.36 342.24 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 461.16 343.92 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 465.36 342.24 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 475.08 343.92 Tm
(and)Tj
/F22 1 Tf
-30.349 -1.243 TD
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 151.08 334.32 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 159.12 330.36 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 172.08 334.32 Tm
<1B>Tj
/F23 1 Tf
-0.30113 -0.87326 TD
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 177.72 330.36 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 181.92 328.08 Tm
<1B>Tj
/F23 1 Tf
0.63236 0 Td
(\()Tj
/F26 1 Tf
0.40652 0 Td
(a)Tj
/F23 1 Tf
0.55708 0 Td
(\))Tj
/F7 1 Tf
10.90909 0 0 10.90909 202.32 330.36 Tm
[(induced)-319(b)33(y)-330(the)-330(pro)-55(jections)-341(from)]TJ
/F22 1 Tf
14.333 0 Td
(W)Tj
/F23 1 Tf
7.97011 0 0 7.97011 369 328.68 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 377.28 330.36 Tm
[(on)33(to)]TJ
/F22 1 Tf
2.255 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 408.24 328.68 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 416.52 330.36 Tm
[(and)-330(\()]TJ
/F22 1 Tf
2.332 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 448.32 328.68 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 453 330.36 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 457.2 334.32 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 462.96 330.36 Tm
[(;)-330(since)]TJ
-29.238 -1.243 TD
[(these)-418(pro)-55(jections)-418(are)-407(the)-418(restrictions)-418(of)-407(the)-418(pro)-55(jections)-407(from)]TJ
/F22 1 Tf
27.335 0 Td
(W)Tj
/F7 1 Tf
1.496 0 Td
[(on)33(to)]TJ
/F22 1 Tf
2.321 0 Td
(V)Tj
/F7 1 Tf
-31.15199 -1.243 TD
(and)Tj
/F22 1 Tf
1.947 0 Td
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 174 307.2 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 179.64 303.24 Tm
(,)Tj
/F22 1 Tf
0.605 0 Td
(f)Tj
/F23 1 Tf
7.97011 0 0 7.97011 191.64 301.56 Tm
(1)Tj
/F24 1 Tf
10.90909 0 0 10.90909 199.44 303.24 Tm
<12>Tj
/F22 1 Tf
1.056 0 Td
(f)Tj
/F7 1 Tf
0.605 0 Td
0.44 Tc
[(.S)440(o)]TJ
/F22 1 Tf
2.101 0 Td
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 247.56 307.2 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 255.6 303.24 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 266.16 301.56 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 270.84 303.24 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 275.04 301.56 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 283.8 303.24 Tm
[(is)-330(a)]TJ
/F22 1 Tf
1.837 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
[(-submo)-33(dule)-319(of)]TJ
/F22 1 Tf
6.501 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 388.44 307.2 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 396.48 303.24 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 413.76 301.56 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 418.8 303.24 Tm
(.)Tj
/F28 1 Tf
0.715 0 Td
(2)Tj
/F6 1 Tf
-25.90499 -2.277 TD
[(Theorem)-385(4.8)]TJ
/F21 1 Tf
6.853 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.76 0 Td
0 Tc
(\()Tj
/F24 1 Tf
(U)Tj
/F22 1 Tf
1.111 0 Td
0.165 Tc
[<3B1B>187(;D)]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.781 0 Td
[(b)55(e)-396(a)-396(satur)55(ate)55(d)-407(mo)55(del)-407(of)-396(DCF)99(A)-385(and)-396(let)]TJ
/F22 1 Tf
17.138 0 Td
(K)Tj
/F7 1 Tf
1.254 0 Td
(=)Tj
/F22 1 Tf
-31.18499 -1.243 TD
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
(K)Tj
/F7 1 Tf
1.309 0 Td
(\))Tj
/F24 1 Tf
0.671 0 Td
0.275 Tc
<1255>Tj
/F21 1 Tf
1.782 0 Td
0.451 Tc
[(.L)506(e)451(t)]TJ
/F22 1 Tf
2.475 0 Td
0 Tc
(tp)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
(a=K)Tj
/F7 1 Tf
3.201 0 Td
(\))Tj
/F21 1 Tf
0.726 0 Td
[(b)55(e)-352(\fnite-dimensional)-352(\(i.e.)]TJ
/F22 1 Tf
11.594 0 Td
[(tr)33(:dg)]TJ
/F7 1 Tf
2.079 0 Td
(\()Tj
/F22 1 Tf
(K)Tj
/F7 1 Tf
1.309 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 446.4 263.16 Tm
-0.03 Tc
[<1B3B>-30(D)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 461.4 264.84 Tm
0 Tc
(=K)Tj
/F7 1 Tf
1.419 0 Td
(\))Tj
/F22 1 Tf
0.671 0 Td
(<)Tj
/F24 1 Tf
-31.18499 -1.243 TD
(1)Tj
/F21 1 Tf
[(\).)-572(L)55(et)]TJ
/F22 1 Tf
4.048 0 Td
(b)Tj
/F21 1 Tf
0.825 0 Td
[(b)55(e)-396(such)-396(that)]TJ
/F22 1 Tf
5.665 0 Td
(b)Tj
/F7 1 Tf
0.77 0 Td
(=)Tj
/F22 1 Tf
1.122 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a=acl)Tj
/F7 1 Tf
2.684 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(b)]TJ
/F7 1 Tf
2.112 0 Td
0 Tc
(\)\)\))Tj
/F21 1 Tf
[(.)-594(Then)]TJ
/F22 1 Tf
4.708 0 Td
(tp)Tj
/F7 1 Tf
0.869 0 Td
(\()Tj
/F22 1 Tf
(b=acl)Tj
/F7 1 Tf
2.585 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(a)]TJ
/F7 1 Tf
2.211 0 Td
0 Tc
(\)\))Tj
/F21 1 Tf
-31.16299 -1.243 TD
[(is)-363(almost-internal)-385(to)]TJ
/F22 1 Tf
9.24 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.53 0 Td
0.209 Tc
(\\C)Tj
/F22 1 Tf
1.463 0 Td
0 Tc
(:)Tj
/F11 1 Tf
-13.233 -2.277 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
[(By)-407(assumption,)]TJ
/F22 1 Tf
7.282 0 Td
[(tr)-33(dg)]TJ
/F7 1 Tf
1.87 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 289.2 197.64 Tm
-0.03 Tc
[<1B3B>-30(D)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 304.08 199.32 Tm
0 Tc
(=K)Tj
/F7 1 Tf
1.419 0 Td
[(\))-407(is)-396(\fnite.)-649(Enlarging)]TJ
/F22 1 Tf
9.647 0 Td
(a)Tj
/F7 1 Tf
[(,)-418(w)33(e)-407(ma)33(y)-407(as-)]TJ
-25.73999 -1.232 TD
[(sume)-451(that)]TJ
/F22 1 Tf
4.972 0 Td
(a)Tj
/F7 1 Tf
0.99 0 Td
[(con)33(tains)-462(a)-462(transcendence)-462(basis)-462(of)]TJ
/F22 1 Tf
15.411 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 401.4 184.2 Tm
-0.03 Tc
[<1B3B>-30(D)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 421.2 185.88 Tm
-0.033 Tc
[(ove)-33(r)]TJ
/F22 1 Tf
2.266 0 Td
0 Tc
(K)Tj
/F7 1 Tf
0.924 0 Td
[(.)-803(Then)]TJ
/F22 1 Tf
-28.59999 -1.243 TD
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F22 1 Tf
0.165 Tc
[(;D)132(a)]TJ
/F24 1 Tf
2.596 0 Td
0 Tc
(2)Tj
/F22 1 Tf
1.045 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 224.52 176.28 Tm
[(al)-15(g)]TJ
/F7 1 Tf
10.90909 0 0 10.90909 240.72 172.32 Tm
(and)Tj
/F22 1 Tf
2.002 0 Td
(D)Tj
/F23 1 Tf
7.97011 0 0 7.97011 271.92 176.28 Tm
(2)Tj
/F7 1 Tf
10.90909 0 0 10.90909 276.6 172.32 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F24 1 Tf
0.77 0 Td
(2)Tj
/F22 1 Tf
1.045 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
[(a;)-165(D)-33(a)]TJ
/F7 1 Tf
[(\).)-627(Hence)-396(w)33(e)-396(ma)33(y)-396(assume)-396(that)]TJ
/F22 1 Tf
-15.807 -1.243 TD
0.033 Tc
(Da)Tj
/F24 1 Tf
1.661 0 Td
0 Tc
(2)Tj
/F22 1 Tf
0.946 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
0.913 0 Td
(\).)Tj
ET
endstream
endobj
12 0 obj
<<
/Length 17787
>>
stream
/GS4 gs
BT
/F7 1 Tf
10.90909 0 0 10.90909 144 722.16 Tm
0 g
(10)Tj
/F11 1 Tf
7.612 0 Td
[(R.)-374(Busamante)]TJ
/F12 1 Tf
5.97758 0 0 5.97758 312.48 722.16 Tm
[(R)60(ev.Mate.T)80(e)60(or.Aplic.)]TJ
/F13 1 Tf
11.46282 0 Td
((2010))Tj
/F14 1 Tf
3.79417 0 Td
(17)Tj
/F15 1 Tf
1.40525 0 Td
((1))Tj
/F7 1 Tf
10.90909 0 0 10.90909 160.92 686.4 Tm
(Let)Tj
/F22 1 Tf
1.76 0 Td
(V)Tj
/F7 1 Tf
1.111 0 Td
[(b)-33(e)-297(the)-308(lo)-33(cus)-308(of)]TJ
/F22 1 Tf
6.633 0 Td
(a)Tj
/F7 1 Tf
0.836 0 Td
-0.033 Tc
[(ove)-33(r)]TJ
/F22 1 Tf
2.112 0 Td
0 Tc
(K)Tj
/F7 1 Tf
1.221 0 Td
(,)Tj
/F22 1 Tf
0.594 0 Td
(W)Tj
/F7 1 Tf
1.386 0 Td
[(the)-308(lo)-33(cus)-297(of)-308(\()]TJ
/F22 1 Tf
5.687 0 Td
[(a;)-165<1B>]TJ
/F7 1 Tf
1.573 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
[(\)\))-330(o)33(v)33(er)]TJ
/F22 1 Tf
4.125 0 Td
(K)Tj
/F7 1 Tf
0.924 0 Td
[(,)-308(th)33(us)]TJ
/F22 1 Tf
-29.51299 -1.243 TD
(V)Tj
/F26 1 Tf
7.97011 0 0 7.97011 152.76 676.8 Tm
<1B>Tj
/F7 1 Tf
10.90909 0 0 10.90909 162 672.84 Tm
[(is)-341(the)-330(lo)-33(cus)-341(of)]TJ
/F22 1 Tf
6.402 0 Td
<1B>Tj
/F7 1 Tf
0.605 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
-0.033 Tc
[(\))-374(ove)-33(r)]TJ
/F22 1 Tf
3.784 0 Td
0 Tc
(K)Tj
/F7 1 Tf
0.924 0 Td
(.)Tj
-11.814 -1.276 TD
(Let)Tj
/F22 1 Tf
1.793 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 186.84 657.2401 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 195.12 658.92 Tm
[(b)-33(e)-330(the)-330(lo)-33(cus)-330(of)]TJ
/F22 1 Tf
6.743 0 Td
(a)Tj
/F7 1 Tf
0.869 0 Td
-0.033 Tc
[(ove)-33(r)]TJ
/F22 1 Tf
2.134 0 Td
0 Tc
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(b)]TJ
/F7 1 Tf
2.112 0 Td
0 Tc
[(\);)-352(let)]TJ
/F22 1 Tf
2.453 0 Td
(b)Tj
/F23 1 Tf
7.97011 0 0 7.97011 369.84 657.2401 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 378.24 658.92 Tm
[(b)-33(e)-319(the)-341(\feld)-319(of)-341(de\fnition)]TJ
-21.472 -1.24299 TD
(of)Tj
/F22 1 Tf
1.144 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 162.84 643.6801 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 167.52 645.36 Tm
[(.)-451(By)-330(4.5)]TJ
/F22 1 Tf
3.905 0 Td
(b)Tj
/F24 1 Tf
0.704 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.011 Tc
[(K;)-154(b)]TJ
/F23 1 Tf
7.97011 0 0 7.97011 265.08 643.6801 Tm
0 Tc
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 270 645.36 Tm
(\).)Tj
-9.999 -1.353 TD
[(By)-286(4.2)-297(for)-286(eac)33(h)]TJ
/F22 1 Tf
6.765 0 Td
0.275 Tc
(m>)Tj
/F7 1 Tf
2.211 0 Td
0 Tc
[(1)-297(there)-286(is)-286(a)-286(\()]TJ
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
7.854 0 Td
0.121 Tc
(\\C)Tj
/F7 1 Tf
1.375 0 Td
0 Tc
[(\)-basis)-297(of)]TJ
/F22 1 Tf
4.224 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 412.68 634.56 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 420.72 630.6 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.814 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 438 635.88 Tm
(\\)Tj
0 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 446.04 630.6 Tm
[(whic)33(h)-286(is)-286(a)]TJ
/F24 1 Tf
-27.68699 -1.24299 TD
(U)Tj
/F7 1 Tf
0.726 0 Td
[(-basis)-220(of)]TJ
/F22 1 Tf
3.707 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 199.44 621 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 207.48 617.04 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 224.64 615.36 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 229.68 617.04 Tm
[(.)-407(Cho)-33(ose)-220(suc)33(h)-220(a)-231(basis)]TJ
/F22 1 Tf
9.262 0 Td
(d)Tj
/F26 1 Tf
7.97011 0 0 7.97011 336.36 615.36 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 346.8 617.04 Tm
[(suc)33(h)-220(that)]TJ
/F22 1 Tf
4.202 0 Td
(d)Tj
/F7 1 Tf
0.803 0 Td
0.275 Tc
(=\()Tj
/F22 1 Tf
1.441 0 Td
0 Tc
(d)Tj
/F23 1 Tf
7.97011 0 0 7.97011 422.76 615.36 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 427.56 617.04 Tm
0.165 Tc
(;d)Tj
/F23 1 Tf
7.97011 0 0 7.97011 438 615.36 Tm
0 Tc
(2)Tj
/F22 1 Tf
10.90909 0 0 10.90909 442.8 617.04 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F7 1 Tf
1.331 0 Td
0 Tc
(\))Tj
/F24 1 Tf
0.726 0.198 TD
(j)Tj
/F22 1 Tf
-0.352 -0.352 TD
(^)Tj
/F26 1 Tf
7.97011 0 0 7.97011 477.24 614.88 Tm
0.015 Tc
[(K;)15(a)]TJ
/F22 1 Tf
10.90909 0 0 10.90909 491.76 617.04 Tm
0 Tc
(b)Tj
/F7 1 Tf
0.429 0 Td
(.)Tj
-32.30699 -1.43 TD
[(Then)-737(for)-737(eac)33(h)]TJ
/F22 1 Tf
7.623 0 Td
(m)Tj
/F7 1 Tf
1.628 0 Td
[(w)33(e)-748(ha)33(v)33(e)-759(an)-748(isomorphism)-737(b)-33(et)33(w)33(een)]TJ
/F22 1 Tf
16.929 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 436.68 605.4 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 444.72 601.44 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F7 1 Tf
0.803 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 461.88 606.84 Tm
(\\)Tj
0 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 475.08 601.44 Tm
(and)Tj
-30.349 -1.331 TD
(\()Tj
/F24 1 Tf
0.308 Tc
(C\\)Tj
/F22 1 Tf
2.145 0 Td
0 Tc
[(F)-143(ix\033)]TJ
/F7 1 Tf
2.299 0 Td
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 196.68 590.88 Tm
(r)Tj
/F29 1 Tf
5.97758 0 0 5.97758 200.52 589.92 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 212.16 586.92 Tm
[(for)-374(some)]TJ
/F22 1 Tf
4.125 0 Td
(r)Tj
/F26 1 Tf
7.97011 0 0 7.97011 262.08 585.2401 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 270.12 586.92 Tm
[(.)-572(Th)33(us)-363(the)-385(image)-385(of)]TJ
/F22 1 Tf
9.306 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 378.72 590.88 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 386.64 586.92 Tm
(\()Tj
/F22 1 Tf
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 397.2 585.2401 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 402 586.92 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 406.2 592.2 Tm
(\\)Tj
0 -0.84315 TD
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 415.32 586.92 Tm
[(in)-374(\()]TJ
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
4.158 0 Td
0.242 Tc
(\\C)Tj
/F7 1 Tf
1.496 0 Td
0 Tc
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 481.2 590.88 Tm
(r)Tj
/F29 1 Tf
5.97758 0 0 5.97758 485.04 589.92 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 144 573.36 Tm
[(is)-341(a)-352(\()]TJ
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
4.785 0 Td
0.22 Tc
(\\C)Tj
/F7 1 Tf
1.474 0 Td
0 Tc
[(\)-subspace)-352(of)-341(\()]TJ
/F22 1 Tf
[(F)-143(ix\033)]TJ
/F24 1 Tf
8.987 0 Td
0.231 Tc
(\\C)Tj
/F7 1 Tf
1.485 0 Td
0 Tc
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 330.72 577.32 Tm
(r)Tj
/F29 1 Tf
5.97758 0 0 5.97758 334.56 576.36 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 345.84 573.36 Tm
[(and)-341(therefore)-352(it)-352(is)-341(de\fned)-330(o)33(v)33(er)]TJ
-18.502 -1.243 TD
[(some)-286(tuple)]TJ
/F22 1 Tf
4.95 0 Td
(e)Tj
/F26 1 Tf
7.97011 0 0 7.97011 203.04 558.12 Tm
(m)Tj
/F24 1 Tf
10.90909 0 0 10.90909 214.08 559.8 Tm
<12>Tj
/F22 1 Tf
1.056 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.42 0 Td
0.11 Tc
(\\C)Tj
/F7 1 Tf
1.364 0 Td
0 Tc
[(;)-297(let)]TJ
/F22 1 Tf
1.969 0 Td
(e)Tj
/F7 1 Tf
0.737 0 Td
0.275 Tc
(=\()Tj
/F22 1 Tf
1.441 0 Td
0 Tc
(e)Tj
/F23 1 Tf
7.97011 0 0 7.97011 317.16 558.12 Tm
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 321.96 559.8 Tm
0.165 Tc
(;e)Tj
/F23 1 Tf
7.97011 0 0 7.97011 331.8 558.12 Tm
0 Tc
(2)Tj
/F22 1 Tf
10.90909 0 0 10.90909 336.72 559.8 Tm
(;)Tj
/F24 1 Tf
0.44 0 Td
0.165 Tc
<010101>Tj
/F7 1 Tf
1.331 0 Td
0 Tc
[(\).)-429(If)]TJ
/F22 1 Tf
2.035 0 Td
<1C>Tj
/F7 1 Tf
0.836 0 Td
[(is)-275(an)-275(automorphism)-275(of)]TJ
-22.308 -1.24299 TD
(\()Tj
/F24 1 Tf
0.385 0 Td
(U)Tj
/F22 1 Tf
0.726 0 Td
0.165 Tc
[<3B1B>187(;D)]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
[(\))-319(\fxing)]TJ
/F22 1 Tf
3.421 0 Td
0.165 Tc
[(K)154(;a)165(;d)165(;e)]TJ
/F7 1 Tf
3.685 0 Td
0 Tc
[(,)-341(then)]TJ
/F22 1 Tf
2.86 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 296.88 550.2 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 304.92 546.2401 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 315.48 544.56 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 320.16 546.2401 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 324.36 544.56 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 332.52 546.2401 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 361.32 550.2 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 369.36 546.2401 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 379.92 544.56 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 384.72 546.2401 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 388.92 544.56 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 393.96 546.2401 Tm
[(\);)-319(on)-297(the)-308(other)-297(hand,)]TJ
/F22 1 Tf
-22.913 -1.24299 TD
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 161.28 536.64 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 169.32 532.68 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 179.88 531 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 184.68 532.68 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 188.88 531 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 193.92 532.68 Tm
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.716 0 Td
0 Tc
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 219.72 536.64 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 227.76 532.68 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 248.52 531 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 253.32 532.68 Tm
(\)\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 261.72 531 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 266.88 532.68 Tm
[(,)-297(th)33(us)-297(for)-286(all)]TJ
/F22 1 Tf
5.566 0 Td
0.286 Tc
(m>)Tj
/F7 1 Tf
2.211 0 Td
0 Tc
(1,)Tj
/F22 1 Tf
1.078 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 370.56 536.64 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 378.6 532.68 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 389.16 531 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 393.96 532.68 Tm
(\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 398.16 531 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 406.2 532.68 Tm
(=)Tj
/F22 1 Tf
1.056 0 Td
(J)Tj
/F26 1 Tf
7.97011 0 0 7.97011 424.8 536.64 Tm
(m)Tj
/F7 1 Tf
10.90909 0 0 10.90909 432.84 532.68 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 453.6 531 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 458.4 532.68 Tm
(\)\))Tj
/F26 1 Tf
7.97011 0 0 7.97011 466.8 531 Tm
(a)Tj
/F7 1 Tf
10.90909 0 0 10.90909 475.08 532.68 Tm
(and)Tj
-30.349 -1.243 TD
[(b)33(y)-341(2.3)]TJ
/F22 1 Tf
3.025 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 193.56 517.44 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 198.24 519.12 Tm
0.308 Tc
(\)=)Tj
/F22 1 Tf
1.76 0 Td
0 Tc
(V)Tj
/F23 1 Tf
7.97011 0 0 7.97011 223.8 517.44 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 228.6 519.12 Tm
[(,)-341(th)33(us)]TJ
/F22 1 Tf
2.827 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(b)Tj
/F23 1 Tf
7.97011 0 0 7.97011 274.32 517.44 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 279.12 519.12 Tm
0.297 Tc
(\)=)Tj
/F22 1 Tf
1.76 0 Td
0 Tc
(b)Tj
/F23 1 Tf
7.97011 0 0 7.97011 303 517.44 Tm
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 311.4 519.12 Tm
[(whic)33(h)-341(implies)-352(that)]TJ
/F22 1 Tf
8.459 0 Td
(b)Tj
/F23 1 Tf
7.97011 0 0 7.97011 408.36 517.44 Tm
(1)Tj
/F24 1 Tf
10.90909 0 0 10.90909 416.28 519.12 Tm
(2)Tj
/F22 1 Tf
0.957 0 Td
(dcl)Tj
/F7 1 Tf
1.265 0 Td
(\()Tj
/F22 1 Tf
0.165 Tc
[(K)154(;a)165(;d)165(;e)]TJ
/F7 1 Tf
4.07 0 Td
0 Tc
(\).)Tj
-31.25099 -1.23199 TD
(Hence)Tj
/F22 1 Tf
2.97 0 Td
(b)Tj
/F24 1 Tf
0.704 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.165 Tc
[(K)154(;a)165(;d)165(;e)]TJ
/F7 1 Tf
4.07 0 Td
0 Tc
[(\).)-484(Since)]TJ
/F22 1 Tf
3.751 0 Td
(e)Tj
/F24 1 Tf
0.748 0 Td
<12>Tj
/F22 1 Tf
1.056 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.519 0 Td
0.209 Tc
(\\C)Tj
/F7 1 Tf
1.793 0 Td
0 Tc
(and)Tj
/F22 1 Tf
1.936 0 Td
(d)Tj
/F24 1 Tf
0.858 0.198 TD
(j)Tj
/F22 1 Tf
-0.352 -0.352 TD
(^)Tj
/F26 1 Tf
7.97011 0 0 7.97011 397.92 503.52 Tm
0.076 Tc
(Ka)Tj
/F22 1 Tf
10.90909 0 0 10.90909 410.64 505.68 Tm
0 Tc
(b)Tj
/F7 1 Tf
[(,)-330(this)-330(pro)33(v)33(es)-341(our)]TJ
-24.442 -1.243 TD
(assertion.)Tj
/F28 1 Tf
4.565 0 Td
(2)Tj
/F7 1 Tf
-3.014 -1.276 TD
[(As)-330(in)-341([8],)-341(w)33(e)-341(deduce)-330(the)-330(dic)33(hotom)33(y)-352(theorem.)]TJ
/F6 1 Tf
-1.551 -2.189 TD
[(Corollary)-385(4.9)]TJ
/F21 1 Tf
7.084 0 Td
(If)Tj
/F22 1 Tf
1.1 0 Td
(tp)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
1.254 0 Td
(a=K)Tj
/F7 1 Tf
1.947 0 Td
(\))Tj
/F21 1 Tf
0.803 0 Td
[(is)-407(of)]TJ
/F22 1 Tf
2.343 0 Td
0.055 Tc
(SU)Tj
/F21 1 Tf
1.463 0 Td
0 Tc
[(-r)55(ank)-418(1)-407(and)-418(\fnite-dimensional,)-440(then)]TJ
-15.994 -1.243 TD
[(it)-363(is)-352(either)-363(1-b)55(ase)55(d)-374(or)-363(non-ortho)55(gonal)-407(to)]TJ
/F22 1 Tf
17.776 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.53 0 Td
0.209 Tc
(\\C)Tj
/F21 1 Tf
1.463 0 Td
0 Tc
(.)Tj
-20.21799 -2.178 TD
[(Pr)55(o)55(of)]TJ
/F7 1 Tf
2.31 0 Td
(:)Tj
-2.31 -1.265 TD
[(W)88(e)-484(suppress)-462(the)-473(set)-473(of)-484(parameters.)-869(Let)]TJ
/F22 1 Tf
18.777 0 Td
(p)Tj
/F7 1 Tf
1.023 0 Td
(=)Tj
/F22 1 Tf
1.287 0 Td
(tp)Tj
/F7 1 Tf
0.869 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
[(\).)-869(If)]TJ
/F22 1 Tf
3.586 0 Td
(p)Tj
/F7 1 Tf
0.968 0 Td
[(is)-473(not)-484(1-)]TJ
-28.06099 -1.243 TD
[(based)-517(there)-517(is)-528(a)-517(tuple)-517(of)-528(realizations)]TJ
/F22 1 Tf
17.457 0 Td
(d)Tj
/F7 1 Tf
1.045 0 Td
(of)Tj
/F22 1 Tf
1.32 0 Td
(p)Tj
/F7 1 Tf
1.023 0 Td
[(and)-517(a)-517(tuple)]TJ
/F22 1 Tf
5.885 0 Td
(c)Tj
/F7 1 Tf
0.957 0 Td
[(suc)33(h)-517(that)]TJ
/F22 1 Tf
-27.68699 -1.243 TD
(c)Tj
/F7 1 Tf
0.715 0 Td
(=)Tj
/F22 1 Tf
1.056 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.385 0 Td
(d=c)Tj
/F7 1 Tf
1.441 0 Td
(\)\))Tj
/F24 1 Tf
1.056 0 Td
<3612>Tj
/F22 1 Tf
1.045 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(d)Tj
/F7 1 Tf
[(\).)-451(Then)]TJ
/F22 1 Tf
4.18 0 Td
(tp)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
(c=d)Tj
/F7 1 Tf
[(\))-297(is)-286(non-algebraic)-297(and)-275(b)33(y)-286(4.8)-286(it)-286(is)]TJ
-15.103 -1.243 TD
[(almost-in)33(ternal)-286(to)]TJ
/F22 1 Tf
7.997 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.376 0 Td
0.066 Tc
(\\C)Tj
/F7 1 Tf
1.32 0 Td
0.418 Tc
[(.A)418(s)]TJ
/F22 1 Tf
2.09 0 Td
0 Tc
(tp)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
1.254 0 Td
(c=d)Tj
/F7 1 Tf
0.275 Tc
[(\)i)275(s)]TJ
/F22 1 Tf
3.036 0 Td
0 Tc
(p)Tj
/F7 1 Tf
[(-in)33(ternal)-264(w)33(e)-264(ha)33(v)33(e)]TJ
/F22 1 Tf
8.074 0 Td
(p)Tj
/F24 1 Tf
0.781 0 Td
(6?)Tj
/F22 1 Tf
1.056 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.376 0 Td
0.066 Tc
(\\C)Tj
/F7 1 Tf
1.32 0 Td
0 Tc
(.)Tj
/F28 1 Tf
-31.67999 -1.243 TD
(2)Tj
/F7 1 Tf
1.551 -1.265 TD
[(W)88(e)-462(conclude)-462(with)-440(an)-451(application)-462(to)-462(de\fnable)-440(groups)-451(of)]TJ
/F21 1 Tf
25.531 0 Td
[(DCF)99(A)]TJ
/F7 1 Tf
0.44 Tc
[(.W)528(e)]TJ
-27.082 -1.243 TD
0 Tc
[(need)-330(the)-341(follo)33(wing)-352(lemmas)-330(on)-341(quan)33(ti\fer-free)-330(stable)-352(groups.)]TJ
/F6 1 Tf
0 -2.497 TD
[(Lemma)-385(4.10)]TJ
/F21 1 Tf
6.622 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.859 0 Td
0 Tc
(M)Tj
/F21 1 Tf
1.573 0 Td
[(b)55(e)-495(a)-506(simple)-506(quanti\fer-fr)55(e)55(e)-495(stable)-506(structur)55(e)-495(which)]TJ
-10.054 -1.243 TD
[(eliminates)-462(imaginaries.)-748(L)55(et)]TJ
/F22 1 Tf
12.815 0 Td
(G)Tj
/F21 1 Tf
1.232 0 Td
[(b)55(e)-451(a)-462(c)55(onne)55(cte)55(d)-473(gr)55(oup,)-484(quanti\fer-fr)55(e)55(e)-462(de-)]TJ
-14.047 -1.243 TD
[(\fnable)-462(in)]TJ
/F22 1 Tf
4.598 0 Td
(M)Tj
/F21 1 Tf
1.54 0 Td
[(de\fne)55(d)-473(over)]TJ
/F22 1 Tf
5.797 0 Td
(A)Tj
/F7 1 Tf
1.21 0 Td
(=)Tj
/F22 1 Tf
1.243 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
(A)Tj
/F7 1 Tf
(\))Tj
/F24 1 Tf
2.002 0 Td
<12>Tj
/F22 1 Tf
1.243 0 Td
(M)Tj
/F21 1 Tf
1.078 0 Td
0.759 Tc
[(.L)814(e)759(t)]TJ
/F22 1 Tf
2.904 0 Td
0 Tc
(c)Tj
/F24 1 Tf
0.891 0 Td
(2)Tj
/F22 1 Tf
1.133 0 Td
(G)Tj
/F21 1 Tf
1.254 0 Td
[(and)-473(let)]TJ
/F22 1 Tf
3.553 0 Td
(H)Tj
/F21 1 Tf
1.375 0 Td
-0.055 Tc
(be)Tj
-31.09699 -1.243 TD
0 Tc
[(the)-440(left)-440(stabilizer)-451(of)]TJ
/F22 1 Tf
9.097 0 Td
(p)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
(x)Tj
/F7 1 Tf
0.418 Tc
(\)=)Tj
/F22 1 Tf
3.465 0 Td
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
1.958 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(c=)55(A)]TJ
/F7 1 Tf
(\))Tj
/F21 1 Tf
0.693 Tc
[(.L)748(e)693(t)]TJ
/F22 1 Tf
5.203 0 Td
0 Tc
(a)Tj
/F24 1 Tf
0.946 0 Td
(2)Tj
/F22 1 Tf
1.089 0 Td
(G)Tj
/F21 1 Tf
1.221 0 Td
(and)Tj
/F22 1 Tf
2.013 0 Td
(b)Tj
/F21 1 Tf
0.869 0 Td
[(r)55(e)55(alize)-451(a)-440(non-)]TJ
-25.86099 -1.243 TD
[(forking)-429(extension)-429(of)]TJ
/F22 1 Tf
9.185 0 Td
(p)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
(x)Tj
/F7 1 Tf
1.463 0 Td
(\))Tj
/F21 1 Tf
0.814 0 Td
(to)Tj
/F22 1 Tf
1.265 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
(Aa)Tj
/F7 1 Tf
1.661 0 Td
(\))Tj
/F21 1 Tf
[(.)-671(Then)]TJ
/F22 1 Tf
4.026 0 Td
(aH)Tj
/F21 1 Tf
1.87 0 Td
[(is)-418(inter)55(de\fnable)-440(over)]TJ
/F22 1 Tf
9.647 0 Td
(A)Tj
/F21 1 Tf
-31.207 -1.232 TD
(with)Tj
/F22 1 Tf
2.09 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F24 1 Tf
0.583 0 Td
<01>Tj
/F22 1 Tf
0.33 0 Td
[(b=)55(A;)-165(a)]TJ
/F7 1 Tf
(\)\))Tj
/F21 1 Tf
[(.)-440(Likewise)-275(with)-297(right)-286(stabilizers)-286(and)-297(c)55(osets)-286(in)-275(plac)55(e)]TJ
-6.952 -1.243 TD
[(of)-363(left)-363(ones,)-352(and)]TJ
/F22 1 Tf
7.436 0 Td
(b)Tj
/F24 1 Tf
0.649 0 Td
<01>Tj
/F22 1 Tf
0.506 0 Td
(a)Tj
/F21 1 Tf
0.88 0 Td
[(inste)55(ad)-374(of)]TJ
/F22 1 Tf
4.576 0 Td
(a)Tj
/F24 1 Tf
0.748 0 Td
<01>Tj
/F22 1 Tf
0.506 0 Td
(b)Tj
/F21 1 Tf
(.)Tj
/F11 1 Tf
-15.301 -2.475 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.265 TD
(Let)Tj
/F22 1 Tf
1.694 0 Td
(q)Tj
/F7 1 Tf
0.726 0 Td
[(b)-33(e)-231(the)-242(quan)33(ti\fer-free)-253(t)33(yp)-33(e)-242(o)33(v)33(er)]TJ
/F22 1 Tf
13.431 0 Td
(M)Tj
/F7 1 Tf
1.32 0 Td
[(whic)33(h)-231(is)-242(the)-242(non-forking)-242(exten-)]TJ
-18.722 -1.243 TD
[(sion)-297(of)]TJ
/F22 1 Tf
3.124 0 Td
(p)Tj
/F7 1 Tf
[(.)-429(Then)]TJ
/F22 1 Tf
3.784 0 Td
(aq)Tj
/F7 1 Tf
1.309 0 Td
[(is)-297(the)-297(non-forking)-297(extension)-308(to)]TJ
/F22 1 Tf
13.53 0 Td
(M)Tj
/F7 1 Tf
1.375 0 Td
(of)Tj
/F22 1 Tf
1.1 0 Td
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
1.958 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a)Tj
/F24 1 Tf
1.056 0 Td
<01>Tj
/F22 1 Tf
0.418 0 Td
[(b=)55(Aa)]TJ
/F7 1 Tf
[(\).)-451(So)]TJ
ET
endstream
endobj
13 0 obj
<<
/Length 12838
>>
stream
/GS4 gs
BT
/F11 1 Tf
10.90909 0 0 10.90909 168.12 722.16 Tm
0 g
[(algebraic)-363(jet)-363(sp)66(a)22(ces)-363(and)-363(zilber)66('s)-363(dichotomy)-363(in)-385(dcf)88(a)]TJ
/F7 1 Tf
28.75399 0 Td
(11)Tj
-30.96499 -3.278 TD
[(w)33(e)-308(m)33(ust)-297(pro)33(v)33(e)-308(that)-319(for)-297(ev)33(ery)-308(automorphism)]TJ
/F22 1 Tf
19.382 0 Td
<1C>Tj
/F24 1 Tf
0.825 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(Aut)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
0.055 Tc
[(M=)110(A)]TJ
/F7 1 Tf
4.279 0 Td
0 Tc
(\),)Tj
/F22 1 Tf
0.99 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(aH)Tj
/F7 1 Tf
1.826 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
(aH)Tj
/F7 1 Tf
-30.52499 -1.243 TD
[(if)-330(and)-330(only)-341(if)]TJ
/F22 1 Tf
5.973 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(aq)Tj
/F7 1 Tf
1.012 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
(aq)Tj
/F7 1 Tf
1.012 0 Td
(.)Tj
-9.108 -1.243 TD
(Since)Tj
/F22 1 Tf
2.629 0 Td
(q)Tj
/F7 1 Tf
0.825 0 Td
(is)Tj
/F22 1 Tf
1.023 0 Td
(A)Tj
/F7 1 Tf
0.748 0 Td
(-de\fnable,)Tj
/F22 1 Tf
4.851 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(q)Tj
/F7 1 Tf
0.484 0 Td
0.308 Tc
(\)=)Tj
/F22 1 Tf
1.771 0 Td
0 Tc
(q)Tj
/F7 1 Tf
0.484 0 Td
[(,)-352(and)]TJ
/F22 1 Tf
2.585 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(aq)Tj
/F7 1 Tf
1.397 0 Td
0.308 Tc
(\)=)Tj
/F22 1 Tf
1.771 0 Td
0 Tc
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F22 1 Tf
1.298 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(q)Tj
/F7 1 Tf
0.869 0 Td
0.319 Tc
(\)=)Tj
/F22 1 Tf
1.782 0 Td
0 Tc
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F22 1 Tf
(q)Tj
/F7 1 Tf
1.782 0 Td
[(.)-506(Th)33(us)]TJ
/F22 1 Tf
-28.98499 -1.243 TD
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(aq)Tj
/F7 1 Tf
1.012 0 Td
0.44 Tc
(\)=)Tj
/F22 1 Tf
2.035 0 Td
0 Tc
(aq)Tj
/F7 1 Tf
1.441 0 Td
[(if)-429(and)-418(only)-440(if)]TJ
/F22 1 Tf
6.347 0 Td
(a)Tj
/F4 1 Tf
7.97011 0 0 7.97011 278.16 649.6801 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 289.56 645.72 Tm
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F22 1 Tf
0.385 0 Td
(q)Tj
/F7 1 Tf
0.924 0 Td
(=)Tj
/F22 1 Tf
1.21 0 Td
(q)Tj
/F7 1 Tf
0.484 0 Td
[(.)-737(But)]TJ
/F22 1 Tf
3.091 0 Td
(H)Tj
/F7 1 Tf
1.342 0 Td
(=)Tj
/F24 1 Tf
1.21 0 Td
(f)Tj
/F22 1 Tf
(x)Tj
/F24 1 Tf
1.507 0 Td
(2)Tj
/F22 1 Tf
1.111 0 Td
(G)Tj
/F7 1 Tf
1.221 0 Td
(:)Tj
/F22 1 Tf
0.704 0 Td
(xq)Tj
/F7 1 Tf
1.496 0 Td
(=)Tj
/F22 1 Tf
1.21 0 Td
(q)Tj
/F24 1 Tf
0.484 0 Td
(g)Tj
/F7 1 Tf
0.495 0 Td
(,)Tj
-31.67999 -1.243 TD
(then)Tj
/F22 1 Tf
2.299 0 Td
(a)Tj
/F4 1 Tf
7.97011 0 0 7.97011 174.84 636.12 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F22 1 Tf
10.90909 0 0 10.90909 186.24 632.16 Tm
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
0.528 0 Td
(\))Tj
/F24 1 Tf
0.715 0 Td
(2)Tj
/F22 1 Tf
0.99 0 Td
(H)Tj
/F7 1 Tf
1.265 0 Td
[(if)-363(and)-352(only)-363(if)]TJ
/F22 1 Tf
6.072 0 Td
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
(a)Tj
/F7 1 Tf
(\))Tj
/F22 1 Tf
1.298 0 Td
(H)Tj
/F7 1 Tf
1.243 0 Td
(=)Tj
/F22 1 Tf
1.1 0 Td
(aH)Tj
/F7 1 Tf
1.441 0 Td
[(,)-374(and)-352(as)]TJ
/F22 1 Tf
3.872 0 Td
(H)Tj
/F7 1 Tf
1.265 0 Td
(is)Tj
/F22 1 Tf
1.034 0 Td
(Aa)Tj
/F7 1 Tf
(-de\fnable,)Tj
/F22 1 Tf
-26.17999 -1.243 TD
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(aH)Tj
/F7 1 Tf
1.441 0 Td
0.286 Tc
(\)=)Tj
/F22 1 Tf
1.727 0 Td
0 Tc
<1C>Tj
/F7 1 Tf
0.55 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F22 1 Tf
0.913 0 Td
(H)Tj
/F7 1 Tf
0.913 0 Td
(.)Tj
/F28 1 Tf
0.726 0 Td
(2)Tj
/F6 1 Tf
-7.59 -2.013 TD
[(Lemma)-385(4.11)]TJ
/F21 1 Tf
6.622 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F22 1 Tf
1.859 0 Td
0 Tc
(M)Tj
/F21 1 Tf
1.573 0 Td
[(b)55(e)-495(a)-506(simple)-506(quanti\fer-fr)55(e)55(e)-495(stable)-506(structur)55(e)-495(which)]TJ
-10.054 -1.24299 TD
[(eliminates)-363(imaginaries.)-462(L)55(et)]TJ
/F22 1 Tf
12.32 0 Td
(G)Tj
/F21 1 Tf
1.144 0 Td
[(b)55(e)-341(a)-363(c)55(onne)55(cte)55(d)-363(gr)55(oup,)-363(quanti\fer-fr)55(e)55(e)-352(de\fn-)]TJ
-13.464 -1.24299 TD
[(able)-440(in)]TJ
/F22 1 Tf
3.421 0 Td
(M)Tj
/F21 1 Tf
1.507 0 Td
[(de\fne)55(d)-440(over)]TJ
/F22 1 Tf
5.731 0 Td
(A)Tj
/F7 1 Tf
1.166 0 Td
(=)Tj
/F22 1 Tf
1.188 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
0.385 0 Td
(A)Tj
/F7 1 Tf
(\))Tj
/F24 1 Tf
1.551 0 Td
<12>Tj
/F22 1 Tf
1.188 0 Td
(M)Tj
/F21 1 Tf
1.078 0 Td
0.682 Tc
[(.L)737(e)682(t)]TJ
/F22 1 Tf
2.794 0 Td
0 Tc
(c)Tj
/F24 1 Tf
0.847 0 Td
(2)Tj
/F22 1 Tf
1.078 0 Td
(G)Tj
/F21 1 Tf
[(,)-451(let)]TJ
/F22 1 Tf
3.014 0 Td
(H)Tj
/F21 1 Tf
1.342 0 Td
[(b)55(e)-440(the)-429(left)]TJ
-27.56599 -1.24299 TD
[(stabilizer)-352(of)]TJ
/F22 1 Tf
5.379 0 Td
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
1.958 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(c=)55(A)]TJ
/F7 1 Tf
(\))Tj
/F21 1 Tf
2.739 0 Td
[(and)-352(let)]TJ
/F22 1 Tf
3.322 0 Td
(a)Tj
/F24 1 Tf
0.803 0 Td
(2)Tj
/F22 1 Tf
0.946 0 Td
(G)Tj
/F21 1 Tf
1.133 0 Td
[(b)55(e)-341(a)-352(generic)-341(over)]TJ
/F22 1 Tf
7.744 0 Td
(A)Tj
/F24 1 Tf
0.946 0 Td
0.187 Tc
([f)Tj
/F22 1 Tf
1.353 0 Td
0 Tc
(c)Tj
/F24 1 Tf
0.429 0 Td
(g)Tj
/F21 1 Tf
[(.)-462(Then)]TJ
/F22 1 Tf
3.861 0 Td
0.077 Tc
(Hc)Tj
/F21 1 Tf
-30.613 -1.243 TD
0 Tc
[(is)-363(inter)55(de\fnable)-374(with)]TJ
/F22 1 Tf
9.416 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(a=)55(A;)-165(c)]TJ
/F24 1 Tf
3.201 0 Td
<01>Tj
/F22 1 Tf
0.495 0 Td
(a)Tj
/F7 1 Tf
(\)\))Tj
/F21 1 Tf
1.661 0 Td
(over)Tj
/F22 1 Tf
2.211 0 Td
(A)Tj
/F24 1 Tf
0.979 0 Td
0.209 Tc
([f)Tj
/F22 1 Tf
1.375 0 Td
0 Tc
(a)Tj
/F24 1 Tf
(g)Tj
/F11 1 Tf
-22.902 -2.013 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
[(W)88(e)-396(ma)33(y)-374(assume)]TJ
/F22 1 Tf
7.469 0 Td
(A)Tj
/F7 1 Tf
1.1 0 Td
(=)Tj
/F24 1 Tf
1.133 0 Td
(;)Tj
/F7 1 Tf
[(.)-572(Let)]TJ
/F22 1 Tf
3.179 0 Td
(p)Tj
/F7 1 Tf
0.847 0 Td
(=)Tj
/F22 1 Tf
1.133 0 Td
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
1.958 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(c=)55(A)]TJ
/F7 1 Tf
[(\).)-572(W)88(e)-396(kno)33(w)-374(that)]TJ
/F22 1 Tf
9.867 0 Td
(H)Tj
/F7 1 Tf
1.287 0 Td
[(is)-374(the)]TJ
-29.52399 -1.243 TD
[(righ)33(t)-286(stabilizer)-297(of)]TJ
/F22 1 Tf
7.689 0 Td
(p)Tj
/F4 1 Tf
7.97011 0 0 7.97011 233.4 497.28 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 244.68 493.32 Tm
[(,)-297(on)-286(the)-286(other)-286(hand,)-286(since)]TJ
/F22 1 Tf
11.286 0 Td
(a)Tj
/F7 1 Tf
0.814 0 Td
[(is)-286(a)-286(generic)-297(of)]TJ
/F22 1 Tf
6.171 0 Td
(G)Tj
/F7 1 Tf
1.067 0 Td
-0.033 Tc
[(we)-319(h)-33(ave)]TJ
/F22 1 Tf
-28.56699 -1.243 TD
0 Tc
(c)Tj
/F24 1 Tf
0.77 0.198 TD
(j)Tj
/F22 1 Tf
-0.352 -0.352 TD
(^)Tj
1.001 0.154 TD
(c)Tj
/F24 1 Tf
0.682 0 Td
<01>Tj
/F22 1 Tf
0.528 0 Td
(a)Tj
/F7 1 Tf
[(.)-572(By)-385(4.10,)]TJ
/F22 1 Tf
5.423 0 Td
0.077 Tc
(Hc)Tj
/F24 1 Tf
1.595 0 Td
0 Tc
<01>Tj
/F22 1 Tf
0.528 0 Td
(a)Tj
/F7 1 Tf
0.913 0 Td
[(is)-374(in)33(terde\fnable)-374(with)]TJ
/F22 1 Tf
9.658 0 Td
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(c)Tj
/F4 1 Tf
7.97011 0 0 7.97011 418.08 483.72 Tm
<00>Tj
/F23 1 Tf
0.82809 0 Td
(1)Tj
/F7 1 Tf
10.90909 0 0 10.90909 429.24 479.76 Tm
(\()Tj
/F22 1 Tf
0.385 0 Td
(c)Tj
/F24 1 Tf
0.693 0 Td
<01>Tj
/F22 1 Tf
0.528 0 Td
(a)Tj
/F7 1 Tf
(\))Tj
/F22 1 Tf
(=c)Tj
/F24 1 Tf
2.101 0 Td
<01>Tj
/F22 1 Tf
0.517 0 Td
(a)Tj
/F7 1 Tf
(\)\).)Tj
-30.37099 -1.243 TD
(Since)Tj
/F22 1 Tf
2.607 0 Td
(H)Tj
/F7 1 Tf
1.254 0 Td
(is)Tj
/F24 1 Tf
1.001 0 Td
(;)Tj
/F7 1 Tf
(-de\fnable,)Tj
/F22 1 Tf
5.335 0 Td
0.077 Tc
(Hc)Tj
/F24 1 Tf
1.562 0 Td
0 Tc
<01>Tj
/F22 1 Tf
0.506 0 Td
(a)Tj
/F7 1 Tf
0.858 0 Td
[(is)-341(in)33(terde\fnable)-330(with)]TJ
/F22 1 Tf
9.537 0 Td
0.077 Tc
(Hc)Tj
/F7 1 Tf
1.683 0 Td
-0.033 Tc
[(ove)-33(r)]TJ
/F22 1 Tf
2.134 0 Td
0 Tc
(a)Tj
/F7 1 Tf
(.)Tj
/F28 1 Tf
1.254 0 Td
(2)Tj
/F6 1 Tf
-27.731 -2.013 TD
[(Corollary)-385(4.12)]TJ
/F21 1 Tf
7.656 0 Td
-0.055 Tc
[(Le)-55(t)]TJ
/F7 1 Tf
1.639 0 Td
0 Tc
(\()Tj
/F24 1 Tf
(U)Tj
/F22 1 Tf
1.111 0 Td
0.165 Tc
[<3B1B>187(;D)]TJ
/F7 1 Tf
2.288 0 Td
0 Tc
(\))Tj
/F21 1 Tf
0.671 0 Td
[(b)55(e)-275(a)-275(mo)55(del)-297(of)-264(DCF)99(A,)-264(and)-286(let)]TJ
/F22 1 Tf
12.309 0 Td
(K)Tj
/F7 1 Tf
1.199 0 Td
(=)Tj
/F22 1 Tf
1.056 0 Td
(acl)Tj
/F7 1 Tf
1.276 0 Td
(\()Tj
/F22 1 Tf
(K)Tj
/F7 1 Tf
1.309 0 Td
(\))Tj
/F24 1 Tf
0.671 0 Td
<12>Tj
-31.18499 -1.243 TD
(U)Tj
/F21 1 Tf
0.726 0 Td
0.649 Tc
[(.L)704(e)649(t)]TJ
/F22 1 Tf
2.75 0 Td
0 Tc
(G)Tj
/F21 1 Tf
1.21 0 Td
[(b)55(e)-418(a)-429(\fnite-dimensional)-440(quanti\fer-fr)55(e)55(e)-429(de\fnable)-429(gr)55(oup,)-451(de\fne)55(d)]TJ
-4.686 -1.243 TD
(over)Tj
/F22 1 Tf
2.233 0 Td
(K)Tj
/F21 1 Tf
0.924 0 Td
0.517 Tc
[(.L)572(e)517(t)]TJ
/F22 1 Tf
2.563 0 Td
0 Tc
(a)Tj
/F24 1 Tf
0.847 0 Td
(2)Tj
/F22 1 Tf
0.979 0 Td
(G)Tj
/F21 1 Tf
1.166 0 Td
[(and)-396(let)]TJ
/F22 1 Tf
3.388 0 Td
(p)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
0.891 0 Td
(x)Tj
/F7 1 Tf
0.319 Tc
(\)=)Tj
/F22 1 Tf
2.365 0 Td
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
1.958 0 Td
0 Tc
(\()Tj
/F22 1 Tf
(a=K)Tj
/F7 1 Tf
2.332 0 Td
(\))Tj
/F21 1 Tf
[(.)-517(Assume)-374(that)]TJ
/F22 1 Tf
7.029 0 Td
(p)Tj
/F21 1 Tf
0.88 0 Td
[(has)-396(trivial)]TJ
-27.55499 -1.243 TD
[(stabilizer.)-473(Then)]TJ
/F22 1 Tf
7.249 0 Td
(p)Tj
/F21 1 Tf
0.858 0 Td
[(is)-352(internal)-374(to)]TJ
/F22 1 Tf
6.039 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.53 0 Td
0.22 Tc
(\\C)Tj
/F21 1 Tf
1.474 0 Td
0 Tc
(.)Tj
/F11 1 Tf
-18.14999 -2.013 TD
[(pr)22(oof:)]TJ
/F7 1 Tf
1.551 -1.243 TD
(Let)Tj
/F22 1 Tf
1.793 0 Td
(b)Tj
/F24 1 Tf
0.715 0 Td
(2)Tj
/F22 1 Tf
0.957 0 Td
(G)Tj
/F7 1 Tf
1.122 0 Td
[(b)-33(e)-330(a)-352(generic)-341(o)33(v)33(er)]TJ
/F22 1 Tf
7.755 0 Td
(K)Tj
/F24 1 Tf
1.144 0 Td
0.22 Tc
([f)Tj
/F22 1 Tf
1.386 0 Td
0 Tc
(a)Tj
/F24 1 Tf
(g)Tj
/F7 1 Tf
[(.)-473(By)-341(4.11)]TJ
/F22 1 Tf
5.456 0 Td
(a)Tj
/F7 1 Tf
0.869 0 Td
[(is)-341(in)33(terde\fnable)-341(with)]TJ
/F22 1 Tf
-22.748 -1.243 TD
0.077 Tc
(Cb)Tj
/F7 1 Tf
1.221 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(b=K)-11(;)-165(a)]TJ
/F24 1 Tf
3.278 0 Td
<01>Tj
/F22 1 Tf
0.418 0 Td
(b)Tj
/F7 1 Tf
[(\)\))-319(o)33(v)33(er)]TJ
/F22 1 Tf
3.619 0 Td
(K)Tj
/F24 1 Tf
1.067 0 Td
0.143 Tc
([f)Tj
/F22 1 Tf
1.309 0 Td
0 Tc
(b)Tj
/F24 1 Tf
(g)Tj
/F7 1 Tf
1.232 0 Td
[(and)-286(b)33(y)-297(4.8,)]TJ
/F22 1 Tf
5.115 0 Td
(tp)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
0.077 Tc
(Cb)Tj
/F7 1 Tf
2.475 0 Td
0 Tc
(\()Tj
/F22 1 Tf
0.033 Tc
[(qf)-77(t)33(p)]TJ
/F7 1 Tf
2.343 0 Td
0 Tc
(\()Tj
/F22 1 Tf
[(b=K)-11(;)-165(a)]TJ
/F24 1 Tf
3.278 0 Td
<01>Tj
/F22 1 Tf
0.418 0 Td
(b)Tj
/F7 1 Tf
0.429 0 Td
(\)\))Tj
/F22 1 Tf
[(=K)-11(;)-165(b)]TJ
/F7 1 Tf
2.992 0 Td
(\))Tj
-31.53699 -1.243 TD
[(is)-308(in)33(ternal)-308(to)]TJ
/F24 1 Tf
5.83 0 Td
0.22 Tc
(C\\)Tj
/F22 1 Tf
1.584 0 Td
0 Tc
[(F)-143(ix\033)]TJ
/F7 1 Tf
2.299 0 Td
[(.)-429(Th)33(us)]TJ
/F22 1 Tf
3.212 0 Td
(tp)Tj
/F7 1 Tf
(\()Tj
/F22 1 Tf
[(a=K)-11(;)-165(b)]TJ
/F7 1 Tf
[(\))-319(is)-308(in)33(ternal)-308(to)]TJ
/F22 1 Tf
10.538 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.464 0 Td
0.165 Tc
(\\C)Tj
/F7 1 Tf
1.419 0 Td
0 Tc
[(;)-308(and)-297(since)]TJ
/F22 1 Tf
-27.34599 -1.243 TD
(a)Tj
/F24 1 Tf
0.858 0.198 TD
(j)Tj
/F22 1 Tf
-0.352 -0.352 TD
(^)Tj
/F26 1 Tf
7.97011 0 0 7.97011 160.56 325.2 Tm
(K)Tj
/F22 1 Tf
10.90909 0 0 10.90909 168.72 327.36 Tm
(b)Tj
/F7 1 Tf
0.429 0 Td
(,)Tj
/F22 1 Tf
0.616 0 Td
(tp)Tj
/F7 1 Tf
0.869 0 Td
(\()Tj
/F22 1 Tf
(a=K)Tj
/F7 1 Tf
2.332 0 Td
[(\))-341(is)-330(in)33(ternal)-341(to)]TJ
/F22 1 Tf
6.644 0 Td
[(F)-143(ix\033)]TJ
/F24 1 Tf
2.53 0 Td
0.22 Tc
(\\C)Tj
/F7 1 Tf
1.474 0 Td
0 Tc
(.)Tj
/F28 1 Tf
0.726 0 Td
(2)Tj
/F20 1 Tf
14.34624 0 0 14.34624 144 293.52 Tm
(References)Tj
/F7 1 Tf
10.90909 0 0 10.90909 149.4 269.16 Tm
[([1])-517(Bustaman)33(te)-297(Medina,)-308(R.F.)-297((2007))-396(\\Di\013eren)33(tially)-319(closed)-297(\felds)-275(of)-297(c)33(har-)]TJ
1.562 -1.243 TD
[(acteristic)-264(zero)-253(with)-242(a)-253(generic)-253(automorphism",)]TJ
/F21 1 Tf
19.833 0 Td
[(R)55(evista)-286(de)-275(Matem\023)506(atic)55(a:)]TJ
-19.833 -1.243 TD
-0.077 Tc
[(Te)-22(o)-77(r)22<13>]TJ
1.969 0 Td
0 Tc
[<1061>-374(y)-352(Aplic)55(aciones)]TJ
/F6 1 Tf
7.81 0 Td
(14)Tj
/F7 1 Tf
[((1):)-462(81{100.)]TJ
-11.341 -1.958 TD
[([2])-517(Bustaman)33(te)-286(Medina,)-297(R.F.)-286((2008))-374(\\Rank)-275(and)-275(dimension)-264(in)-275(di\013erence-)]TJ
1.562 -1.243 TD
[(di\013eren)33(tial)-352(\felds",)]TJ
/F21 1 Tf
8.448 0 Td
[(Submitte)55(d)]TJ
/F7 1 Tf
(.)Tj
-10.01 -1.947 TD
[([3])-517(Chatzidakis,)-418(Z.;)-429(Hrusho)33(vski,)-418(E.)-396((1999))-660(\\Mo)-33(del)-407(theory)-407(of)-396(di\013erence)]TJ
1.562 -1.243 TD
(\felds",)Tj
/F21 1 Tf
3.531 0 Td
[(T)77(r)55(ansactions)-407(of)-385(the)-385(A)22(meric)55(an)-385(Mathematic)55(al)-407(So)55(ciety)]TJ
/F6 1 Tf
23.089 0 Td
(351)Tj
/F7 1 Tf
1.716 0 Td
((8):)Tj
-28.33599 -1.243 TD
(2997{3071.)Tj
ET
endstream
endobj
14 0 obj
<<
/Length 2944
>>
stream
/GS4 gs
BT
/F7 1 Tf
10.90909 0 0 10.90909 144 722.16 Tm
0 g
(12)Tj
/F11 1 Tf
7.612 0 Td
[(R.)-374(Busamante)]TJ
/F12 1 Tf
5.97758 0 0 5.97758 312.48 722.16 Tm
[(R)60(ev.Mate.T)80(e)60(or.Aplic.)]TJ
/F13 1 Tf
11.46282 0 Td
((2010))Tj
/F14 1 Tf
3.79417 0 Td
(17)Tj
/F15 1 Tf
1.40525 0 Td
((1))Tj
/F7 1 Tf
10.90909 0 0 10.90909 149.4 686.4 Tm
[([4])-517(Eisen)33(bud,)-473(D.)-462((1995))]TJ
/F21 1 Tf
11.407 0 Td
[(Commutative)-484(A)22(lgebr)55(a)]TJ
/F7 1 Tf
[(.)-814(Springer-V)88(erlag,)-495(New)]TJ
-9.845 -1.243 TD
[(Y)88(ork.)]TJ
-1.562 -2.068 TD
[([5])-517(Mark)33(er,)-363(D.;)-374(Messmer,)-363(M.;)-363(Pilla)33(y)88(,)-385(A.)-352((1996))]TJ
/F21 1 Tf
21.021 0 Td
[(Mo)55(del)-374(The)55(ory)-396(of)-374(Fields)]TJ
/F7 1 Tf
10.153 0 Td
(,)Tj
-29.61199 -1.24299 TD
[(v)33(olume)-341(5)-341(of)]TJ
/F21 1 Tf
5.412 0 Td
[(L)55(e)55(ctur)55(e)-374(Notes)-352(in)-363(L)55(o)55(gic)]TJ
/F7 1 Tf
[(.)-451(Springer-V)88(erlag,)-352(Berlin.)]TJ
-6.974 -2.05699 TD
[([6])-517(Mark)33(er,)-264(D.)-231((2000))-297(\\Mo)-33(del)-242(theory)-231(of)-231(di\013eren)33(tial)-242(\felds",)-297(in:)-396(D.)-231(Hask)33(ell,)]TJ
1.562 -1.243 TD
[(A.)-319(Pilla)33(y)-330(&)-319(C.)-319(Steinhorn)-297((Eds.))]TJ
/F21 1 Tf
14.124 0 Td
[(Mo)55(del)-352(The)55(ory,)-363(A)22(lgebr)55(a,)-352(and)-352(Ge)55(ome-)]TJ
-14.124 -1.24299 TD
(try)Tj
/F7 1 Tf
[(,)-297(v)33(olume)-286(39)-286(of)]TJ
/F21 1 Tf
7.557 0 Td
[(Math.)-308(Sci.)-308(R)55(es.)-308(Inst.)-308(Publ.)]TJ
/F7 1 Tf
11.506 0 Td
[(,)-286(Cam)33(bridge)-275(Univ.)-286(Press,)]TJ
-19.06299 -1.24299 TD
[(Cam)33(bridge:)-451(53{63.)]TJ
-1.562 -2.06799 TD
[([7])-517(Pierce,)-352(D.;)-341(Pilla)33(y)88(,)-363(A.)-341((1998))-484(\\A)-341(note)-352(on)-330(the)-341(axioms)-341(for)-341(di\013eren)33(tially)]TJ
1.562 -1.243 TD
[(closed)-341(\felds)-330(of)-330(c)33(haracteristic)-374(zero",)]TJ
/F21 1 Tf
15.796 0 Td
[(J.)-363(A)22(lgebr)55(a)]TJ
/F6 1 Tf
4.763 0 Td
(204)Tj
/F7 1 Tf
[((1):)-473(108{115.)]TJ
-22.121 -2.057 TD
[([8])-517(Pilla)33(y)88(,)-286(A.)-242((2002))-319(\\Mo)-33(del-theoretic)-275(consequences)-242(of)-253(a)-242(theorem)-242(of)-242(Cam-)]TJ
1.562 -1.243 TD
[(pana)-330(and)-330(F)88(ujiki",)]TJ
/F21 1 Tf
8.118 0 Td
[(F)77(undamenta)-385(Mathematic)55(ae)]TJ
/F6 1 Tf
12.133 0 Td
(174)Tj
/F7 1 Tf
[((2):)-473(187{192.)]TJ
-21.81299 -2.068 TD
[([9])-517(Pilla)33(y)88(,)-341(A.;)-330(Ziegler,)-330(M.)-319((2003))-429(\\Jet)-330(spaces)-319(of)-308(v)55(arieties)-330(o)33(v)33(er)-330(di\013eren)33(tial)]TJ
1.562 -1.243 TD
[(and)-385(di\013erence)-407(\felds",)]TJ
/F21 1 Tf
10.186 0 Td
[(Sele)55(cta)-429(Mathematic)55(a.)-429(New)-407(Series)]TJ
/F6 1 Tf
15.015 0 Td
(9)Tj
/F7 1 Tf
[((4):)-594(579{)]TJ
-25.20099 -1.243 TD
(599.)Tj
-2.057 -2.057 TD
[([10])-517(Shafarevic)33(h,)-330(I.R.)-330((1977))]TJ
/F21 1 Tf
12.881 0 Td
[(Basic)-352(A)22(lgebr)55(aic)-352(Ge)55(ometry)]TJ
/F7 1 Tf
[(.)-451(Springer-V)88(erlag,)]TJ
-10.824 -1.243 TD
(Berlin.)Tj
ET
endstream
endobj
15 0 obj
<<
/Nums[0<>]
>>
endobj
16 0 obj
<<
/Differences[16/dotlessi 19/acute 40/parenleft/parenright 45/hyphen 48/zero/one/two/three/four 57/nine/colon 65/A 77/M 82/R 84/T 97/a 99/c/d/e 105/i 108/l/m/n/o/p 114/r/s/t/u/v 121/y 123/endash]
/BaseEncoding/MacRomanEncoding
/Type/Encoding
>>
endobj
17 0 obj
<<
/Length1 3828
/Length 3828
/Subtype/Type1C
>>
stream
BDLGPJ+CMCSC10 Eø øøøø LND
™ûŽúÉù‚
‹‹
‹‹ Î Ê ° Ï IP_1.0Copyright (C) 1997 American Mathematical Society. All Rights ReservedCMCSC10Computer Modern V o
O M Q " Z ‘ S P 5 D } N . E B U T J W F 3 " ¦2„õZªïiè^©ˆT [Âøa ¶
‹
â›äO¹
vÿþïÇ&u§Ó÷÷$¡÷ðɤâñ÷^ò÷›÷åݹM#ûEhVo-“Ïb°†§¤®¯pŸnsk}_.îK÷÷çèïÜJÚû ÷±¯ÚÆÜ0Ä&$8S;j¡x¨ªŸ¡¨½\‹}¸§Îœ¹¼Âp6‹HaXmhr‰L‡yŠ…‹‹€‹€’‹œ‹û§ v÷OÅ¥÷«÷Å÷OÅû«Q&u§¯çà¡ø$¤Åå÷”åø(÷¹ûŠûbPyQŒ®n·“¨œªsšu{m‚dJÀ`è÷÷÷÷j÷šûÖ&=_kjk^_u_ChMÀSh²iÛå®Ú¥–û8x^‹Æhu²‹½¾ÍŒ´¨´«¢¨ ½Ó¨BˆŒŸY‹:}@f#+&‹ª÷ªøuw÷ßÒø&ùŸ‹‘{ŠŠ~ûÖügl÷®4g‰€>tlŽ°Ì‹²²Ë‹ˆ°ªt>‰–¯âöª Døüû˜i}¤ør¤÷Ó÷²¤øm÷Fû5XGm%—÷*÷¡´‘ΤŠnR‰uuSŒmrÏ…`ûmr‹f~:”Û:÷÷ËñÔŒ÷ž³Œ¥¡¸¤‰rVŠ…onŒorÓ‹Vt& v÷“¡™ø ø®÷“¡ü uûdûyvú|w÷–Å÷Ð÷Ž÷òûq÷*€„‡‡…‡†ŒŠà<êûûœB„0i%bû
KNhj‰ˆ‰ˆ‹ˆ‹…‡’‹•‹÷r÷)‹÷óûdûyvú|w÷Å÷þû„ŽŠŽˆŽ^µû÷÷Ì÷Ç÷÷¿¼Ž’‡Ž…~Z[xz#ûYû2û6ûñ÷pû+˜‘Ž’&‹ªø°ªËw÷ŒÕ÷Öù£‹tZZJ|Al¤Ã‹¦Ãü›i‹}+hlŽ¯æ‹´´æ‹ˆ¯ªh+‹™&u¡ù¡ÄÞ÷¤Þøƒ÷Ôí‚ÕfÑÔeEªJGEiCfnQ|Nû
FŽ-µ>,Àä„«½Ú㺲ÖäÓûoûÔdL¡ëv~È‹äÊҋΖÄïŸÑ®¨Ñ~,¢™V‹:DK‹8Pû
t=„t&‹Ø÷ôôðªÍô÷tæøz÷Brˆz‚M~€„„@‹}‹ûU¼·ÝÖœ›¹¯›ÊÅÆÁ‹ç‹÷ )Øû‹û‹=0‹1‹S½‹Ž‹œ‹®—‹´‹¥y¥h‹ˆ…‹ŠˆÇ õÎçÀ@3RsG=8ûmûy‹‰‹tøi‹¤ød¤÷§÷Û§÷Uø‰˜‚‰‹xûr£§‹„Ÿüt‹VCrŒ ¸Ÿš¹Š‰¤¤C‹À¢÷ú•÷ÎüH“€Ž‹‘‹™‹’žø¢‹ÀÓ¤Šv^‰w|]ŒrrÓ‹Vtû½û!‹¤ød¤÷Óøm÷Vr;ƒ2û Lh†Ž³ø½š‹Ö¤ŠnK‰mrYŒgrÎ…büb†…Hrø/3‹¤÷e¢÷|¤÷ Ð÷á÷Q÷~÷ïßÊ×Ó?Ðûû£rÎ…büb†…HrŒ¨Ä¡¡Ã‰Š©¤H†‘´ˆ÷M÷Q³Ž®Ð÷‹?cd‹>û÷:‹ª÷\ªøZwøCùJ„Šz{‰…~†ûqüé‚t{^2ŠlŒ ³³µÄ‰ŠœªXt¥£‘‹—»÷÷žÄû-~‹‰‹ˆnS‹qlŽ¯Ñ‹±¶¹Š‰µªyK”§û²ø ÷ûÞûˆi‹¤ød¤÷¤Ðøzø7¯Á¬™²¤‰voŠvpoŒpr¡‰’{|ƒ„€ûûJû÷_†’„•‹•Ÿ¨‹—¤ŠqI‰{pcŒmr¿—…q÷?ûûb†…HrŒ©»§¨¿‰Š¥¤G‡‘·÷ûꋤød¤÷Ó÷OøM¶Ò¤ŠiW‰qqWŒirÒ†`ü`††DrŒ¿¥¥¿‰Š¤D†¶ÿÿÐ8‘w™¤÷q¡÷q¤÷ Ð÷sáÔ¤|÷ÿ÷“ÑɸÈÑ2Ìû
û„rÎ…büb†…HrŒ©»§¨¿‰Š¥¤H†‘´÷Bºå¤¥Šlª u‹s_S‹y«ly³|¸ËšÉŸ‹•~€Š‚‡N„gŠ„w‚˜–…ƒ›…§~˃®¾@¨2˜3÷F¤••Ž’¦‹Õàˆ d†Cûv}¥ø¤¾á÷þáøÝ÷“÷)û÷û(û)û
ûû)û+÷
û
÷&÷&÷
÷
÷+ûŸû‡DûÄ÷Y÷P÷¼ÎÏ÷YûOûYûRD÷ ‹ªøû°÷ðäù^ù9ýxûu¤÷<™Ÿ¥÷1ž¨‹‰•¡ˆ‹tü£i‹}"clŽ´ñ‹¹¹ò‹ˆ´ªc"‹™ø£¢‹—¡Ž•¨‹ž÷0 qû<™¤ûÝ‹õ÷oõõõ÷hø¨s£nnssnn£s¨¨££¨ûÙ¨s£nnssnn£s¨¨££¨N}¤ø€¤¾áø£ø°øŒ›‹“…Š‰ƒdXv¡Z´@‹û+ûûû,û,÷û÷+÷Úó┋’~€‹…Š!„5O7Yû+¦÷o÷r÷/£¸ÔàWûž„Œ…•˜‹ž& vø¦v÷Qw÷{÷Vø+ù‘—”›œzžx|„ƒz}b[YPleœxød¤÷§ø5Ë÷^ø„„…‹vû
rÎ…bûét‹VCrŒ ¸Ÿš¹Š‰¤¤C‹À¢øŒŒ÷Oü`‚‚•‹•””÷RøgŒŠü0b†…HrŒŸ¼®®¯‰Š¬¤H†‘´ø´‘Τû
tˆ‹xƒû?ü8÷苪ùª÷6§ø¿Ü÷šù-„…‹vû=l£Ø€güˆp‹\$lŒ®¼¬¬¼‰Š®ª$‹º¦ø±ŒŒ÷”ý ‚‚•‹•””÷—ùŒŠüÓg‰€>slŽ°Ï‹²²Î‹ˆ°ªs>‰–¯ø£¯–Ø£ªû=tˆ‹xƒû|üÍv‹¤ød¤÷ Ð÷ÄÞ¸ø–rÎ…büb†…Hr÷÷!õ÷÷÷$÷û$û G³Ž®Øá¶\y™¡o¡a&9|avku{`Y/>h†Ž³i‹¤÷$¤÷åw÷Ýø‘›…†‘€}‰…~†û5ü1€pz^L‰r¡¨Œ¡œ¹‰ŠŸ¤aˆ”“‹ä÷c¡S“w˜i‹…og‹zrŒ¦ÆŸ²‰Š£¤S‚®~ûnøèû…ûON‹¤ø^ª÷˜Óø±øü}û=¤÷”Ÿ÷ÃŽ‹`ü c‡€>vrŽ²Æ‹³³Æ‹ˆ²¤v>‡–³ø ¶Ž‹Ã÷ ¡zû”¤ûW}¤øƒ¡¾¾÷’¾øøŒ›‹“…ŠŠu|††|‡…e°]—b‹0‹IG‹=‹S«j—©mŸ‡çvÁ~•‰¢v‡¦p‹_‹YdUF‹qU®`^®ˆ¼Š¦Š“ƒŒˆ‹~‹‹„‹yû{‹ƒ•‘ŒŒ¡š•š‘¨q¿tÌ‹ì‹ÉØ‹Ú‹Êd³‹Œf±{Ž6Ÿvh“…YŸ{²‹©‹¹³¼Î‹÷û k„‹…–˜‹žûꋤød¤÷Ó÷OøM¶Ò¤ŠiW‰qqWŒirÒ†`ü`††DrŒ¿¥¥¿‰Š¤D†¶i•vøˆ¤øŠø;¦Ê¸šŒ¤‰vpŠvpoŒpr®ˆ’vx€ˆƒ†€û"ûæû*÷üƒ‹‹¦‹œ¤ŠqO‰xqbŒpr‘„j™÷NüL‘~„˜‹™‘™‘3‹¤÷x¤÷d§÷Ó÷0¤ø¥÷Vrû
zs[ûû h†Ž³÷MÑÕ—wH¤÷[rHwAE÷9³Ž®ñ÷¥hû–¤x÷=üQrÎ…büb†…Hrø]÷-u¡‹ª÷À¡÷¿ª÷4á÷Åòó£|øj÷è÷¨ËÍÏìûÞû+ûØl£Ø€gü£g‰€>slŽ¯Ò‹²²Ò‹ˆ¯ªs>‰–¯÷‘º÷Á«w{œ±f‹rEF‹g¶dk°Ã‚®ÛžÝ§‘‹–~€‹‚„Š=ƒb€vV„¸÷y€Ñ‡¤k«v¡kžd–$˜û
÷—¦”£ŽŒ”ª‹Ÿâ÷‹û) D`ûu¡ù?¡ûS™÷–ª
Ó¤‘Óœ
7’ ‹ùendstream
endobj
18 0 obj
<<
/StemV 72
/XHeight 705
/Ascent 683
/Type/FontDescriptor
/Flags 34
/Descent -22
/FontName/BDLGPJ+CMCSC10
/FontBBox[14 -250 1077 750]
/StemH 0
/CapHeight 666
/ItalicAngle 0
/FontFile3 17 0 R
>>
endobj
19 0 obj
<<
/Widths[308 0 0 549 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 442 442 0 0 0 375 0 0 549 549 549 549 549 0 0 0 0 549 321 0 0 0 0 0 0 816 0 0 0 0 0 0 0 0 0 0 0 990 0 0 0 0 803 0 790 0 0 0 0 0 0 0 0 0 0 0 0 616 0 589 629 562 0 0 0 308 0 0 509 749 616 629 562 0 602 455 589 616 616 0 0 616 0 549]
/Subtype/Type1
/LastChar 123
/FirstChar 16
/FontDescriptor 18 0 R
/Encoding 16 0 R
/Type/Font
/BaseFont/BDLGPJ+CMCSC10
/Name/F0
>>
endobj
20 0 obj
<<
/Differences[49/one 55/seven]
/BaseEncoding/MacRomanEncoding
/Type/Encoding
>>
endobj
21 0 obj
<<
/Length1 445
/Length 445
/Subtype/Type1C
>>
stream
HSXVBM+CMBX9 Fø øøøø LN?
QûŽ«ù‚
‹‹
‹‹ Ë Ç Ð¹ IN]1.0Copyright (C) 1997 American Mathematical Society. All Rights ReservedCMBX9Computer Modern s¹ÿÿ p N”vø¤÷÷Z÷øÉøç”–Œ‘Ž¨ûxvû ‘Ž€wŠ’‰–Xhû•¾à–š‘Œ‘š×‹Ÿ÷:%û ‹‰vl9ûyû‹G‹E‰•‹¦‹›š ‹‹Ä‹÷—÷
ÌÔN‹¼ø‚¼Ëw÷†÷ø ù¡‹–n‰‹„‚R> ‹wwZŸ£ÁŽœÃü–û#ZŽ±÷
‹¸º÷
‹ˆ´¼û%—ùB—û’”÷_Ÿû]’¼
÷ ³”÷ §
Œ
7’ ‹ùendstream
endobj
22 0 obj
<<
/StemV 117
/XHeight 698
/Ascent 686
/Type/FontDescriptor
/Flags 262148
/Descent -194
/FontName/HSXVBM+CMBX9
/FontBBox[-58 -250 1195 750]
/StemH 0
/CapHeight 656
/ItalicAngle 0
/FontFile3 21 0 R
>>
endobj
23 0 obj
<<
/Widths[589 0 0 0 0 0 589]
/Subtype/Type1
/LastChar 55
/FirstChar 49
/FontDescriptor 22 0 R
/Encoding 20 0 R
/Type/Font
/BaseFont/HSXVBM+CMBX9
/Name/F1
>>
endobj
24 0 obj
<<
/Differences[16/dotlessi 19/acute 39/quoteright 97/a/b/c/d/e/f/g/h/i/j 108/l/m/n/o/p 114/r/s/t 121/y/z]
/BaseEncoding/MacRomanEncoding
/Type/Encoding
>>
endobj
25 0 obj
<<
/Length1 2837
/Length 2837
/Subtype/Type1C
>>
stream
IQJJST+CMCSC10 Eø øøøø LND
™ûŽúÉù‚
‹‹
‹‹ Î Ê ý°
ð IP_1.0Copyright (C) 1997 American Mathematical Society. All Rights ReservedCMCSC10Computer Modern ‘ } G Z N P I [ E O Q T U K D J S C F H M B P ~ äk Ræ(~ÝWºsÊ&؉øbú E ¿ÿþïÇûò‹¤ød¤÷Ó÷OøM¶Ò¤ŠiW‰qqWŒirÒ†`ü`††DrŒ¿¥¥¿‰Š¤D†¶( vø¦v÷Qw÷{÷Vø+ù‘—”›œzžx|„ƒz}b[YPleœxû‹¤÷n¤÷n§÷Ó÷,¤øqø“üFrÎ…büb†…HrŒ¬À¤«É‰Š¨¤@|‹½÷<ÎÕ–vI¤÷[rI€vAH÷C³Ž®ê÷¨kû•¤ÿÿÛUT‹¤ød¤÷¤Ðøzø7¯Á¬™²¤‰voŠvpoŒpr¡‰’{|ƒ„€ûûJû÷_†’„•‹•Ÿ¨‹—¤ŠqI‰{pcŒmr¿—…q÷?ûûb†…HrŒ©»§¨¿‰Š¥¤G‡‘·÷ÿ `©x‹¤ød¤÷§ø5Ë÷^ø„„…‹vû
rÎ…bûét‹VCrŒ ¸Ÿš¹Š‰¤¤C‹À¢øŒŒ÷Oü`‚‚•‹•””÷RøgŒŠü0b†…HrŒŸ¼®®¯‰Š¬¤H†‘´ø´‘Τû
tˆ‹xƒû?ü8{}¥ø¤¾á÷þáøÝ÷“÷)û÷û(û)û
ûû)û+÷
û
÷&÷&÷
÷
÷+ûŸû‡DûÄ÷Y÷P÷¼ÎÏ÷YûOûYûRDÿÿÛUT‹¤÷z¤÷e¤÷Ó÷ƒÓø†øN´‘ΤŠnR‰uuSŒmrÎ…bû6ûƒ÷6´‘ΤŠnR‰uuSŒmrÎ…büb†…HrŒ¨Ä¡¡Ã‰Š©¤H†‘´÷K÷ƒûKb†…HrŒ¨Ä¡¡Ã‰Š©¤H†‘´ûÝ vø4v÷Uõ÷a¡÷`ø÷Œ…‹‚…&NSxy††‹‰‰…†‘–à×÷
Âu½]hypqqœp¯¦™œ‘ÿÿl7Ì‹§øa¤¾ø(øPøw’•‹Ž™„‹xûöƒû=¤÷‘½ï÷ûÉü\„‹ˆ‹†|‘‹Ÿø—÷]r …zIû!ût‹¤ød¤÷ Ð÷ÄÞ¸ø–rÎ…büb†…Hr÷÷!õ÷÷÷$÷û$û G³Ž®Øá¶\y™¡o¡a&9|avku{`Y/>h†Ž³ÿÿÛUT‹¤ød¤÷§÷Û§÷Uø‰˜‚‰‹xûr£§‹„Ÿüt‹VCrŒ ¸Ÿš¹Š‰¤¤C‹À¢÷ú•÷ÎüH“€Ž‹‘‹™‹’žø¢‹ÀÓ¤Šv^‰w|]ŒrrÓ‹Vtû½/‹¤÷e¢÷|¤÷ Ð÷á÷Q÷~÷ïßÊ×Ó?Ðûû£rÎ…büb†…HrŒ¨Ä¡¡Ã‰Š©¤H†‘´ˆ÷M÷Q³Ž®Ð÷‹?cd‹>ûûR}¤øƒ¡¾¾÷’¾øøŒ›‹“…ŠŠu|††|‡…e°]—b‹0‹IG‹=‹S«j—©mŸ‡çvÁ~•‰¢v‡¦p‹_‹YdUF‹qU®`^®ˆ¼Š¦Š“ƒŒˆ‹~‹‹„‹yû{‹ƒ•‘ŒŒ¡š•š‘¨q¿tÌ‹ì‹ÉØ‹Ú‹Êd³‹Œf±{Ž6Ÿvh“…YŸ{²‹©‹¹³¼Î‹÷û k„‹…–˜‹žQ‹¤ø^ª÷˜Óø±øü}û=¤÷”Ÿ÷ÃŽ‹`ü c‡€>vrŽ²Æ‹³³Æ‹ˆ²¤v>‡–³ø ¶Ž‹Ã÷ ¡zû”¤ûu}¡±Ü÷þ¤¹Þ÷Ð÷Œ÷9[qlue“§t¯’¤š¢ytuw}nVÀ^ÓÎͲΗŒ‘‹¨œ÷¬È‹Á¤ˆgU‹†€7ŒprÓ€dQ}¤ø€¤¾áø£ø°øŒ›‹“…Š‰ƒdXv¡Z´@‹û+ûûû,û,÷û÷+÷Úó┋’~€‹…Š!„5O7Yû+¦÷o÷r÷/£¸ÔàWûž„Œ…•˜‹žûò‹¤ød¤÷Ó÷OøM¶Ò¤ŠiW‰qqWŒirÒ†`ü`††DrŒ¿¥¥¿‰Š¤D†¶X‘w™¤÷q¡÷q¤÷ Ð÷sáÔ¤|÷ÿ÷“ÑɸÈÑ2Ìû
û„rÎ…büb†…HrŒ©»§¨¿‰Š¥¤H†‘´÷Bºå¤¥Šlª u‹s_S‹y«ly³|¸ËšÉŸ‹•~€Š‚‡N„gŠ„w‚˜–…ƒ›…§~˃®¾@¨2˜3÷F¤••Ž’¦‹Õàˆ d†CûD‹¤÷{¡÷g¤÷
Í÷šÞ¹ø–rÎ…büb†…Hr÷Â÷ÑÏÑÌKÂ4–ҚĸÅÊEËûû#û€÷<³Ž®ëæš=sgqB#ûu÷*à¦?a^jG0)h†Ž³/‹¤÷x¤÷d§÷Ó÷0¤ø¥÷Vrû
zs[ûû h†Ž³÷MÑÕ—wH¤÷[rHwAE÷9³Ž®ñ÷¥hû–¤x÷=üQrÎ…büb†…Hrø]ÿÿ÷l}¤÷?¤÷¼¤¾á÷ÞÓø¯÷²‘¿¤‰jcŠqgQ‹ŽhrŸ×€cmt‹sct~ui„nNû$¬÷i÷o÷+¦¼ÔßWûž„Œ…•˜‹ž÷=›‹“…Š‰ƒdXf´V¡T‹û)ûû
û-û)÷û÷0®Õ²}”©l–”‹“šû‹¤ød¤÷Óøm÷Vr;ƒ2û Lh†Ž³ø½š‹Ö¤ŠnK‰mrYŒgrÎ…büb†…Hrø/ÿÿÛUT‹¤÷$¤÷åw÷Ýø‘›…†‘€}‰…~†û5ü1€pz^L‰r¡¨Œ¡œ¹‰ŠŸ¤aˆ”“‹ä÷c¡S“w˜i‹…og‹zrŒ¦ÆŸ²‰Š£¤S‚®~ûnøèû…ûOu¡ù?¡ûS™÷–ª
Ó¤‘Óœ
7’ ‹ùendstream
endobj
26 0 obj
<<
/StemV 72
/XHeight 705
/Ascent 683
/Type/FontDescriptor
/Flags 34
/Descent -22
/FontName/IQJJST+CMCSC10
/FontBBox[14 -250 1077 750]
/StemH 0
/CapHeight 666
/ItalicAngle 0
/FontFile3 25 0 R
>>
endobj
27 0 obj
<<
/Widths[300 0 0 551 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 321 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 613 579 592 627 558 537 641 613 300 425 0 516 746 613 634 558 0 599 460 592 0 0 0 0 613 502]
/Subtype/Type1
/LastChar 122
/FirstChar 16
/FontDescriptor 26 0 R
/Encoding 24 0 R
/Type/Font
/BaseFont/IQJJST+CMCSC10
/Name/F2
>>
endobj
28 0 obj
<<
/Differences[46/period 66/B 70/F 77/M 82/R 97/a 100/d/e 105/i 108/l/m/n/o 115/s/t/u]
/BaseEncoding/MacRomanEncoding
/Type/Encoding
>>
endobj
29 0 obj
<<
/Length1 2109
/Length 2109
/Subtype/Type1C
>>
stream
AVUMRM+CMCSC10 Eø øøøø LND
™ûŽúÉù‚
‹‹
‹‹ Î Ê ï° IP_1.0Copyright (C) 1997 American Mathematical Society. All Rights ReservedCMCSC10Computer Modern J . F N U T V # ' E M B O P 3 P æPá8ñb×õ^½~ôFÿþïÇûñ‹¤ød¤÷Ó÷OøM¶Ò¤ŠiW‰qqWŒirÒ†`ü`††DrŒ¿¥¥¿‰Š¤D†¶÷싪ùª÷6§ø¿Ü÷šù-„…‹vû=l£Ø€güˆp‹\$lŒ®¼¬¬¼‰Š®ª$‹º¦ø±ŒŒ÷”ý ‚‚•‹•””÷—ùŒŠüÓg‰€>slŽ°Ï‹²²Î‹ˆ°ªs>‰–¯ø£¯–Ø£ªû=tˆ‹xƒû|üÍ3‹¤÷x¤÷d§÷Ó÷0¤ø¥÷Vrû
zs[ûû h†Ž³÷MÑÕ—wH¤÷[rHwAE÷9³Ž®ñ÷¥hû–¤x÷=üQrÎ…büb†…Hrø]苤ød¤÷§ø5Ë÷^ø„„…‹vû
rÎ…bûét‹VCrŒ ¸Ÿš¹Š‰¤¤C‹À¢øŒŒ÷Oü`‚‚•‹•””÷RøgŒŠü0b†…HrŒŸ¼®®¯‰Š¬¤H†‘´ø´‘Τû
tˆ‹xƒû?ü8Q‹¤ø^ª÷˜Óø±øü}û=¤÷”Ÿ÷ÃŽ‹`ü c‡€>vrŽ²Æ‹³³Æ‹ˆ²¤v>‡–³ø ¶Ž‹Ã÷ ¡zû”¤ûP}¤øƒ¡¾¾÷’¾øøŒ›‹“…ŠŠu|††|‡…e°]—b‹0‹IG‹=‹S«j—©mŸ‡çvÁ~•‰¢v‡¦p‹_‹YdUF‹qU®`^®ˆ¼Š¦Š“ƒŒˆ‹~‹‹„‹yû{‹ƒ•‘ŒŒ¡š•š‘¨q¿tÌ‹ì‹ÉØ‹Ú‹Êd³‹Œf±{Ž6Ÿvh“…YŸ{²‹©‹¹³¼Î‹÷û k„‹…–˜‹že}¤ør¤÷Ó÷²¤øm÷Fû5XGm%—÷*÷¡´‘ΤŠnR‰uuSŒmrÏ…`ûmr‹f~:”Û:÷÷ËñÔŒ÷ž³Œ¥¡¸¤‰rVŠ…onŒorÓ‹Vt÷‹ª÷Í¡÷²ª÷5Þ÷öïÅù?l£Ø€gü£g‰€>slø*÷ëäéß:Øû˜ìÙÉØä(ÛûûTûÑ÷Š¬’º÷ñ´9SEP=û ûã\‰’¬÷¥÷]ò½2DAO< ûÝ‹õõõ÷hÀ¨s£nnssnn£s¨¨££¨Ê‹ª÷ºª÷¹÷2ä÷`¤ùù<üÎl£Ø€gü g‰€>slŽ®Ù‹²´æ‹ˆ¯ªj,‹˜®÷Šéí—l5¤÷r5l)-÷‘¬’º÷÷/§Uû ›¤o‹¤ød¤÷ Ð÷ÄÞ¸ø–rÎ…büb†…Hr÷÷!õ÷÷÷$÷û$û G³Ž®Øá¶\y™¡o¡a&9|avku{`Y/>h†Ž³û‹¤ød¤÷Óøm÷Vr;ƒ2û Lh†Ž³ø½š‹Ö¤ŠnK‰mrYŒgrÎ…büb†…Hrø/e‹¤÷$¤÷åw÷Ýø‘›…†‘€}‰…~†û5ü1€pz^L‰r¡¨Œ¡œ¹‰ŠŸ¤aˆ”“‹ä÷c¡S“w˜i‹…og‹zrŒ¦ÆŸ²‰Š£¤S‚®~ûnøèû…ûOe‹¤ød¤÷§÷Û§÷Uø‰˜‚‰‹xûr£§‹„Ÿüt‹VCrŒ ¸Ÿš¹Š‰¤¤C‹À¢÷ú•÷ÎüH“€Ž‹‘‹™‹’žø¢‹ÀÓ¤Šv^‰w|]ŒrrÓ‹Vtû½y}¥ø¤¾á÷þáøÝ÷“÷)û÷û(û)û
ûû)û+÷
û
÷&÷&÷
÷
÷+ûŸû‡DûÄ÷Y÷P÷¼ÎÏ÷YûOûYûRD÷-u¡‹ª÷À¡÷¿ª÷4á÷Åòó£|øj÷è÷¨ËÍÏìûÞû+ûØl£Ø€gü£g‰€>slŽ¯Ò‹²²Ò‹ˆ¯ªs>‰–¯÷‘º÷Á«w{œ±f‹rEF‹g¶dk°Ã‚®ÛžÝ§‘‹–~€‹‚„Š=ƒb€vV„¸÷y€Ñ‡¤k«v¡kžd–$˜û
÷—¦”£ŽŒ”ª‹Ÿâ÷‹û) D`ûu¡ù?¡ûS™÷–ª
Ó¤‘Óœ
7’ ‹ùendstream
endobj
30 0 obj
<<
/StemV 72
/XHeight 705
/Ascent 683
/Type/FontDescriptor
/Flags 34
/Descent -22
/FontName/AVUMRM+CMCSC10
/FontBBox[14 -250 1077 750]
/StemH 0
/CapHeight 666
/ItalicAngle 0
/FontFile3 29 0 R
>>
endobj
31 0 obj
<<
/Widths[321 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 773 0 0 0 713 0 0 0 0 0 0 994 0 0 0 0 803 0 0 0 0 0 0 0 0 0 0 0 0 0 0 612 0 0 622 562 0 0 0 301 0 0 512 743 612 632 0 0 0 462 592 612]
/Subtype/Type1
/LastChar 117
/FirstChar 46
/FontDescriptor 30 0 R
/Encoding 28 0 R
/Type/Font
/BaseFont/AVUMRM+CMCSC10
/Name/F3
>>
endobj
32 0 obj
<<
/Differences[0/minus 3/asteriskmath 20/lessequal 48/prime 50/element 68/D 106/bar]
/BaseEncoding/MacRomanEncoding
/Type/Encoding
>>
endobj
33 0 obj
<<
/Length1 917
/Length 917
/Subtype/Type1C
>>
stream
UKBBJP+CMSY8 Mø ø ø!ø"øáJ_ LNr
mþO¡ùŸ
‹‹
‹‹ ÷ ó ¢ ~ "%jo~primelessequalelementasteriskmath1.0Copyright (C) 1997 American Mathematical Society. All Rights ReservedCMSY8Computer Modern ‡ ]ˆ %‰ ¦Š 9 a ÌDªÑdü Évøšwª÷‡÷Ÿør––©o£mcjˆûüFŠ‰‡}‹Š~ª‚’‘–ûñûyvú|w÷¹÷>ù^™‹¡tt‹u}þ4}‹u¢¢‹¡™÷Fû>¹÷Nvùwäùù_ù—‘”‘˜˜•~‡‰‹…€üÞû¯}„„…‹}•†•†øÝû¯˜„‹‹˜••˜™ü»÷Ÿø«ü¡™¡‹¢¢u‹}üÓ}u‹tt¡‹™÷F‹ÅøËÅùkä÷y÷‡÷ì÷A÷©ÝfÌ?³¹3&‹10D‹d2ûOz8„…‰‘ ¼¦¢“—²š·÷.‘zû”GûHYûl‚jq‹~‹ƒ‘‹œ‹÷¼ùë÷osûXûjûbûûxK÷÷¢¢÷v’Òÿ :UTK¹÷‰¹÷‰¹äºàøÚ÷w™¡‹¢¢u‹}üR÷%™÷ï÷"÷<™¡‹¢¢u‹}û?û@û*ûûFûF÷*û÷@÷?™¡‹¢¢u‹}û<û"ûï÷%}÷F v÷w¹äùùP÷w™¡‹¢¢u‹}üÓ}u‹tt¡‹™ûÂvøCw÷€Å÷¬÷t¥yË_¤y¥y‹“‹‹—›‹š‹‘€s–û»÷$Ë•˜‘ž‘‰¤hû%(š÷+œˆ¢o‹y}|}Žšû,ûå~”…‹‡‹y{|x˜…•‡÷$Lû$K‡~…‹x…r®÷%î|û0†„‡”t£¦¡œ‰s£ù? û“¹
乚‹ùendstream
endobj
34 0 obj
<<
/StemV 89
/XHeight 704
/Ascent 683
/Type/FontDescriptor
/Flags 4
/Descent -118
/FontName/UKBBJP+CMSY8
/FontBBox[-30 -955 1185 779]
/StemH 0
/CapHeight 683
/ItalicAngle -14
/FontFile3 33 0 R
>>
endobj
35 0 obj
<<
/Widths[828 0 0 527 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 828 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 286 0 708 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 828 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 301]
/Subtype/Type1
/LastChar 106
/FirstChar 0
/FontDescriptor 34 0 R
/Encoding 32 0 R
/Type/Font
/BaseFont/UKBBJP+CMSY8
/Name/F4
>>
endobj
36 0 obj
<<
/Differences[48/zero/one/two 53/five/six 57/nine/colon/semicolon 65/A 79/O 82/R 99/c/d/e 105/i 112/p 114/r/s/t 118/v]
/BaseEncoding/MacRomanEncoding
/Type/Encoding
>>
endobj
37 0 obj
<<
/Length1 2943
/Length 2943
/Subtype/Type1C
>>
stream
XXZXEO+CMTI12 Lø øøøøáJÿ LN}
gûúãù‚
‹‹
‹‹ Ó Ï ü° Z IO^1.0Copyright (C) 1997 American Mathematical Society. All Rights ReservedCMTI12Computer Modern U 0 T S Q " E W J D F 3 x ÑSÖ=¿ïk¯M¼õ—
ݟ [
0ûÀûÝ•wø0¨÷Vw÷
Â÷”ø&Þœ•‹–„‹z<³÷1ŒŒ”‹”„šxr‚u|‡dû16y‚‹x“‹›ÜCû´†w‹‹‡]¦aÂí½÷(”‚‹‡€Š‰€†ld)J|}’¬š¢šòv¢ù<¡÷&ÝøgÙù™øR÷%6÷ûû]û_û‚û{û$áû÷÷Z÷a÷|÷ü"üP2QÝ÷È¢÷8Ü÷éÎܵËÞÏIûûWûû´ûIû(v¦ø8w÷
Óµ£÷
È÷ÁÙ÷t÷â÷³Ð÷Ÿ¬©¨‚l“Z‰‹b‰x™œµ‹ÉÉV™bQ/lû05ûxû@WJû÷÷÷
÷)÷$²u÷ûH_Z`o¦ûÜWwººã¼÷n÷Ó‹>~enûrV€…a9>ûŒ•wÜÕ÷4ËÓwÕÙ÷K¼øøg‡‰m‡€’}Ÿ¢œ¹c±Kûh%`fžv”œ{ž†¶¤†¾‹T‹ps3û‹g‹Y™€º»‹´‹‹ y“~‹ƒ‹d‡‹T‹NÄhЋ÷ ·÷ÁáD›[–p‘g“¸¥¡ÏÜ´¨vk’ûñû@v÷Uì÷ì÷Wï÷»ø |rkomox˜w¦¬¦ª¦ûüz9\Qhh~‹‰‹‰‹‡…‹‹÷÷‹÷‹†¨j‹k‹po‹l‹o ž‹‹‹ŒŒ’Œ‹‘Žû(v¦°Õ÷wø:£÷7Î÷‘ÆøH÷Ëû Mû f[rfª}®Ž—¥œž}•z„c‰PHÑ®âÖÏÏ¿ì÷£÷BÓ©‹÷%ûûûû%û'd¢û÷ǹ²À¬ûCC‹Ú•¹÷™©Ã¥ºÀËÊ@{B_û‚ûû(ŠwùBw÷Æ÷ËÄø³ø…§‹÷ ûûLüTCP› ÷ÜÙÄ÷Æ«Ñ»÷@êûºü†`l¯ÉÚÕ÷ȶ×ɯ»¢¦¼}8.?û—…x`|_û+û(v˪w÷Âw÷Ýw÷8¦÷ w÷9Í÷õ÷Ž¤™£œ£œÐÀºÃ‹ç‹ëLÑ2‹û'‹<û_‹J‹j˜o®‹Ú‹³÷‹®‹ ª‹‡‹„‡‹…‰‹‰Ž†’|Œ|ˆohûLxˆ›œÎÔ÷Q÷¸·j