Mathematics > Group Theory
[Submitted on 23 Apr 2018 (v1), last revised 12 May 2018 (this version, v2)]
Title:Existence of equivariant models of G-varieties
View PDFAbstract: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.
Submission history
From: Mikhail Borovoi [view email][v1] Mon, 23 Apr 2018 14:39:40 UTC (15 KB)
[v2] Sat, 12 May 2018 09:47:04 UTC (15 KB)
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