Finiteness properties of local cohomology for F-pure local rings
arXiv:1204.1539
Abstract
In this paper, we show that for an -pure local ring $(R,\m)$, all local cohomology modules $H_{\m}^i(R)$ have finitely many Frobenius compatible submodules. This answers positively an open question raised by F.Enescu and M.Hochster. We also prove that if $(R,\m)$ is excellent and is -pure on the punctured spectrum, then all local cohomology modules have finite length in the category of -modules with Frobenius action. Finally, we show that the property that all $H_{\m}^(R)$ have finitely many Frobenius compatible submodules passes to localizations.
Final version