FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION. (7th December 2018) - MA, LINQUAN; QUY, PHAM HUNG
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.