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

Abstract

We prove that Schubert varieties are globally F F -regular in the sense of Karen Smith. We apply this result to the category of equivariant and holonomic D {\mathcal {D}} -modules on flag varieties in positive characteristic. Here recent results of Blickle are shown to imply that the simple D {\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.