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FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION

Published online by Cambridge University Press:  07 September 2017

LINQUAN MA
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84102, USA email lquanma@math.utah.edu
PHAM HUNG QUY
Affiliation:
Department of Mathematics, FPT University, and Thang Long Institute of Mathematics and Applied Sciences, Ha Noi, Vietnam email quyph@fe.edu.vn

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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Article
Copyright
© 2017 Foundation Nagoya Mathematical Journal  

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Footnotes

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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FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION
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