A prime-characteristic analogue of a theorem of Hartshorne-Polini
arXiv:1905.12584
Abstract
Let be an -finite Noetherian regular ring containing an algebraically closed field of positive characteristic, and let be an $\F$-finite $\F$-module over in the sense of Lyubeznik (for example, any local cohomology module of ). We prove that the -dimension of the space of $\F$-module morphisms $M \rightarrow E(R/\fm)$ (where $\fm$ is any maximal ideal of and $E(R/\fm)$ is the -injective hull of $R/\fm$) is equal to the -dimension of the Frobenius stable part of $\Hom_R(M,E(R/\fm))$. This is a positive-characteristic analogue of a recent result of Hartshorne and Polini for holonomic $\D$-modules in characteristic zero. We use this result to calculate the $\F$-module length of certain local cohomology modules associated with projective schemes.
Minor changes to improve exposition. Comments welcome!