Existence of equivariant models of G-varieties
Abstract
Let k0 be a field of characteristic 0, and let k be a fixed algebraic closure of k0. Let G be an algebraic k-group, and let Y be a G-variety over k. Let G0 be a k0 -model (k0 -form) of G. We ask whether Y admits a G0 -equivariant k0 -model Y0 of Y. We assume that Y admits a Gq -equivariant k0 -model Yq, where Gq is an inner form of G0. We give a Galois-cohomological criterion for the existence of a G0 -equivariant k0 -model Y0 of Y. We apply this criterion to spherical homogeneous varieties Y=G/H.
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