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Acta Mathematica Vietnamica

F-Stable Secondary Representations and Deformation of F-Injectivity

Alessandro De Stefani , icon-email Linquan Ma

Abstract

We prove that deformation of F-injectivity holds for local rings (R,m) that admit secondary representations of  Hmi(R) which are stable under the natural Frobenius action. As a consequence, F-injectivity deforms when (R,m) is sequentially Cohen–Macaulay (or more generally when all the local cohomology modules Hmi(R) have no embedded attached primes). We obtain some additional cases if R/m is perfect or if R is N-graded.