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arXiv · 1603.04705

Embeddings of spherical homogeneous spaces in characteristic p

Rudolf Tange
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Abstract

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power, compatible with certain subvarieties. We also look at cohomology vanishing and show the existence of rational G-equivariant resolutions by toroidal embeddings. We show that the class of homogeneous spaces for which our results hold contains the symmetric homogeneous spaces in characteristic not 2 and is closed under parabolic induction.

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Rudolf Tange. 2016-03-15. Embeddings of spherical homogeneous spaces in characteristic p. https://arxiv.org/abs/1603.04705

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