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arXiv · 1204.1539

Finiteness properties of local cohomology for F-pure local rings

Linquan Ma
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Abstract

In this paper, we show that for an $F$-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 $F$-pure on the punctured spectrum, then all local cohomology modules have finite length in the category of $R$-modules with Frobenius action. Finally, we show that the property that all $H_{\m}^(R)$ have finitely many Frobenius compatible submodules passes to localizations.

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Linquan Ma. 2013-08-01. Finiteness properties of local cohomology for F-pure local rings. https://arxiv.org/abs/1204.1539

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