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Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors
We prove the existence of a Galois closure for towers of torsors under finite group schemes over a proper, geometrically connected and geometrically reduced algebraic stack X over a field k. This is done by describing the ...
Models of torsors over affine spaces
Let X := A n R be the n-dimensional affine space over a discrete valuation ring R with fraction field K. We prove that any pointed torsor Y over A n K under the action of an affine finite-type group scheme can be extended ...
The pseudo-fundamental group scheme
Let X be any scheme defined over a Dedekind scheme S with a given section x ∈ X (S). We prove the existence of a pro-finite S-group scheme א (X,x) and a universal א (X,x)-torsor dominating all the pro-finite pointed torsors ...