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arXiv · 1606.02059

Frobenius actions on local cohomology modules and deformation

Linquan Ma·Pham Hung Quy
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Abstract

Let $(R,m)$ be a Noetherian local ring of characteristic $p>0$. We introduce and study $F$-full and $F$-anti-nilpotent singularities, both are defined in terms of the Frobenius actions on the local cohomology modules of $R$ supported at the maximal ideal. We prove that if $R/(x)$ is $F$-full or $F$-anti-nilpotent for a nonzerodivisor $x\in R$, then so is $R$. We use these results to obtain new cases on the deformation of $F$-injectivity.

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Linquan Ma, Pham Hung Quy. 2016-06-07. Frobenius actions on local cohomology modules and deformation. https://arxiv.org/abs/1606.02059

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