EQUIVARIANT MODELS OF SPHERICAL VARIETIES

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Abstract

Let G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G/H be a spherical homogeneous space of G, and let Y′ be a spherical embedding of Y. Let k0 be a subfield of k. Let G0 be a k0-model (k0-form) of G. We show that if G0 is an inner form of a split group and if the subgroup H of G is spherically closed, then Y admits a G0-equivariant k0-model. If we replace the assumption that H is spherically closed by the stronger assumption that H coincides with its normalizer in G, then Y and Y′ admit compatible G0-equivariant k0-models, and these models are unique.

Original languageEnglish
Pages (from-to)391-439
Number of pages49
JournalTransformation Groups
Volume25
Issue number2
DOIs
StatePublished - 1 Jun 2020

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