Global F-regularity of Schubert varieties with applications to D-modules
Algebraic Geometry
2007-06-13 v3 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.math/0402052,
title = {Global F-regularity of Schubert varieties with applications to D-modules},
author = {Niels Lauritzen and Ulf Raben-Pedersen and Jesper Funch Thomsen},
journal= {arXiv preprint arXiv:math/0402052},
year = {2007}
}