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Models of torsors and the fundamental group scheme
dc.creator | Antei, Marco | |
dc.creator | Emsalem, Michel | |
dc.date.accessioned | 2021-11-24T20:07:34Z | |
dc.date.available | 2021-11-24T20:07:34Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/models-of-torsors-and-the-fundamental-group-scheme/6CCB905236E4D15B0EE6136E486914F9 | |
dc.identifier.issn | 2152-6842 | |
dc.identifier.uri | https://hdl.handle.net/10669/85333 | |
dc.description.abstract | Given a relative faithfully at pointed scheme over the spectrum of a discrete valuation ring X !S, this paper is motivated by the study of the natural morphism from the fundamental group scheme of the generic ber X to the generic ber of the fundamental group scheme of X. Given a torsor T !X under an a ne group scheme G over the generic ber of X, we address the question of nding a model of this torsor over X, focusing in particular on the case where G is nite. We provide several answers to this question, showing for instance that, when X is integral and regular of relative dimension 1, such a model exists on some model X0 of X obtained by performing a nite number of N eron blowups along a closed subset of the special ber of X. Furthermore, we show that when G is etale, then we can nd a model of T !X under the action of some smooth group scheme. In the rst part of the paper, we show that the relative fundamental group scheme of X has an interpretation as the Tannaka Galois group of a Tannakian category constructed starting from the universal torsor. | es_ES |
dc.language.iso | eng | es_ES |
dc.source | Nagoya Mathematical Journal, vol.230, pp.18-34 | es_ES |
dc.subject | Torsor | es_ES |
dc.subject | Fundamental group scheme | es_ES |
dc.subject | Models | es_ES |
dc.title | Models of torsors and the fundamental group scheme | es_ES |
dc.type | artículo original | |
dc.identifier.doi | 10.1017/nmj.2016.67 | |
dc.description.procedence | UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA) | es_ES |
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