FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION. (7th December 2018) - MA, LINQUAN; QUY, PHAM HUNG
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 nonzero divisor xR, then so is R . We use these results to obtain new cases on the deformation of F -injectivity.