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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.

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  1. Raymond and Beverly Sackler, School of Mathematical Sciences, Tel Aviv University, 6997801, Tel Aviv, Israel

    MIKHAIL BOROVOI

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  1. MIKHAIL BOROVOI
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Correspondence to MIKHAIL BOROVOI.

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With an appendix by Giuliano Gagliardi.

Partially supported by the Hermann Minkowski Center for Geometry and by the Israel Science Foundation, grant No. 870/16.

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BOROVOI, M. EQUIVARIANT MODELS OF SPHERICAL VARIETIES. Transformation Groups 25, 391–439 (2020). https://doi.org/10.1007/s00031-019-09531-w

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