Existence of equivariant models of spherical varieties and other G-varieties

Mikhail Borovoi; Giuliano Gagliardi

paper

Existence of equivariant models of spherical varieties and other G-varieties

arXiv:1810.08960

Abstract

Let $k_{0}$ be a field of characteristic $0$ with algebraic closure $k$ . Let $G$ be a connected reductive $k$ -group, and let $Y$ be a spherical variety over $k$ (a spherical homogeneous space or a spherical embedding). Let $G_{0}$ be a $k_{0}$ -model ( $k_{0}$ -form) of $G$ . We give necessary and sufficient conditions for the existence of a $G_{0}$ -equivariant $k_{0}$ -model of $Y$ .

This preprint supersedes arXiv:1804.08475. V1: 39 pages. V2: 44 pages; a section on spherical embeddings has been added, and therefore the title and abstract have been changed. V3: 60 pages; a section on horospherical homogeneous spaces has been added. V4: 64 pages; the final version to appear in IMRN