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

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

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

Authors

Lauritzen, Niels

Raben-Pedersen, Ulf

Thomsen, Jesper Funch

Description

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.