Models of torsors and the fundamental group scheme
Loading...
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