Embeddings of spherical homogeneous spaces in characteristic p

Embeddings of spherical homogeneous spaces in characteristic p Let G be a reductive group over an algebraically closed field of characteristic $$p>0$$ p > 0 . We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a $$(p-1)$$ ( p - 1 ) -th power, compatible with certain subvarieties. We show the existence of rational G-equivariant resolutions by toroidal embeddings, and give results about cohomology vanishing and surjectivity of restriction maps of global sections of line bundles. We show that the class of homogeneous spaces for which our results hold contains the symmetric homogeneous spaces in characteristic $$\ne 2$$ ≠ 2 and is closed under parabolic induction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Embeddings of spherical homogeneous spaces in characteristic p

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-017-1897-9
Publisher site
See Article on Publisher Site

Abstract

Let G be a reductive group over an algebraically closed field of characteristic $$p>0$$ p > 0 . We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a $$(p-1)$$ ( p - 1 ) -th power, compatible with certain subvarieties. We show the existence of rational G-equivariant resolutions by toroidal embeddings, and give results about cohomology vanishing and surjectivity of restriction maps of global sections of line bundles. We show that the class of homogeneous spaces for which our results hold contains the symmetric homogeneous spaces in characteristic $$\ne 2$$ ≠ 2 and is closed under parabolic induction.

Journal

Mathematische ZeitschriftSpringer Journals

Published: May 12, 2017

References

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