Frobenius actions on local cohomology modules and deformation

Linquan Ma; Pham Hung Quy

Frobenius actions on local cohomology modules and deformation

Commutative Algebra 2017-05-09 v2

Authors: Linquan Ma , Pham Hung Quy

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.

Keywords

Noetherian local ring Frobenius action local cohomology module F-full singularity F-anti-nilpotent singularity F-injectivity deformation

Cite

@article{arxiv.1606.02059,
  title  = {Frobenius actions on local cohomology modules and deformation},
  author = {Linquan Ma and Pham Hung Quy},
  journal= {arXiv preprint arXiv:1606.02059},
  year   = {2017}
}

Comments

14 pages, final version

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