Existence of equivariant models of G-varieties
arXiv:1804.08475
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.
14 pages, typos corrected