Existence of equivariant models of G-varieties
Group Theory
2018-05-15 v2 Algebraic Geometry
Abstract
Let k_0 be a field of characteristic 0, and let k be a fixed algebraic closure of k_0. Let G be an algebraic k-group, and let Y be a G-variety over k. Let G_0 be a k_0 -model (k_0 -form) of G. We ask whether Y admits a G_0 -equivariant k_0 -model Y_0 of Y. We assume that Y admits a G_q -equivariant k_0 -model Y_q, where G_q is an inner form of G_0. We give a Galois-cohomological criterion for the existence of a G_0 -equivariant k_0 -model Y_0 of Y. We apply this criterion to spherical homogeneous varieties Y=G/H.
Keywords
Cite
@article{arxiv.1804.08475,
title = {Existence of equivariant models of G-varieties},
author = {Mikhail Borovoi},
journal= {arXiv preprint arXiv:1804.08475},
year = {2018}
}
Comments
14 pages, typos corrected