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

2018/10/21 by Borovoi, Mikhail, Gagliardi, Giuliano
#12G05 #14G20 #14G25 #14G27 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Primary: 14M27. Secondary: 14M17

paper · doi:10.48550/arxiv.1810.08960

Abstract

Let k₀ 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 G₀ be a k₀-model (k₀-form) of G. We give necessary and sufficient conditions for the existence of a G₀-equivariant k₀-model of Y.

Related

• Existence of equivariant models of G-varieties
• Spherical varieties over large fields
• Equivariant K-theory of smooth projective spherical varieties
• Embeddings of spherical homogeneous spaces in characteristic p
• Pl ucker relations and spherical varieties: application to model varieties