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Global F-regularity of Schubert varieties with applications to D-modules

Niels Lauritzen·Ulf Raben-Pedersen·Jesper Funch Thomsen
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Abstract

We prove that Schubert varieties are globally F-regular in the sense of Karen Smith. We apply this result to the category of equivariant and holonomic D-modules on flag varieties in positive characteristic. Here recent results of Blickle are shown to imply that the simple D-modules coincide with local cohomology sheaves with support in Schubert varieties. Using a local Grothendieck-Cousin complex we prove that the decomposition of local cohomology sheaves with support in Schubert cells is multiplicity free.

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Niels Lauritzen, Ulf Raben-Pedersen, Jesper Funch Thomsen. 2007-05-30. Global F-regularity of Schubert varieties with applications to D-modules. https://arxiv.org/abs/math/0402052

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