Logo Kérwá
 

Models of torsors and the fundamental group scheme

Loading...
Thumbnail Image

Date

Authors

Antei, Marco
Emsalem, Michel

Journal Title

Journal ISSN

Volume Title

Publisher

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.

Description

Keywords

Torsor, Fundamental group scheme, Models

Citation

https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/models-of-torsors-and-the-fundamental-group-scheme/6CCB905236E4D15B0EE6136E486914F9

Collections

Endorsement

Review

Supplemented By

Referenced By