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

Lauritzen, Niels; Raben-Pedersen, Ulf; Thomsen, Jesper

doi:10.1090/S0894-0347-05-00509-6

Global $F$-regularity of Schubert varieties with applications to $\mathcal {D}$-modules
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by Niels Lauritzen, Ulf Raben-Pedersen and Jesper Funch Thomsen

J. Amer. Math. Soc. 19 (2006), 345-355

DOI: https://doi.org/10.1090/S0894-0347-05-00509-6

Published electronically: December 2, 2005

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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 ${\mathcal {D}}$-modules on flag varieties in positive characteristic. Here recent results of Blickle are shown to imply that the simple ${\mathcal {D}}$-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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