On the injective dimension of F-finite modules and holonomic D-modules

Abstract

Let $R$ be a regular local ring containing a field $k$ of characteristic $p$ and $M$ be an $\mathcal{F}$-finite module. In this paper, we study the injective dimension of $M$. We prove that ${\dim }_R(M)-1\le {inj.dim}_R(M)$. If $R=k[[x_1,\dots ,x_n]]$ where $k$ is a field of characteristic $0$ we prove the analogous result for a class of holonomic $\mathcal{D}$-modules which contains local cohomology modules.

15 pages. comments welcome