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FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION

  • LINQUAN MA (a1) and PHAM HUNG QUY (a2)
Abstract

Let $(R,\mathfrak{m})$ 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 nonzero divisor $x\in R$ , then so is $R$ . We use these results to obtain new cases on the deformation of $F$ -injectivity.

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L. Ma is supported in part by the NSF grant DMS #1600198 and NSF CAREER grant DMS #1252860/1501102, and was partially supported by a Simons Travel grant when preparing this article. P. H. Quy is partially supported by a fund of Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2017.10. This paper was written while Pham Hung Quy was visiting Vietnam Institute for Advanced Study in Mathematics. He would like to thank the VIASM for hospitality and financial support.

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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
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