FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION. (7th December 2018)

• Record Type: Journal Article
• Authors: MA, LINQUAN; QUY, PHAM HUNG
• Is Part Of: Nagoya mathematical journal. Volume 232(2018)
• Page Start: 55
• Page End: 75
• Publication Date: 2018-12-07
• Subjects: 13A35, -- 13D45, -- 14B05; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1017/nmj.2017.20
• Languages: English
• ISSNs: 0027-7630

Abstract

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.