logo_acta

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 $(R,\mathfrak{m})$ that admit secondary representations of  $H^i_{\mathfrak{m}}(R)$ which are stable under the natural Frobenius action. As a consequence, F-injectivity deforms when $(R,\mathfrak{m})$ is sequentially Cohen–Macaulay (or more generally when all the local cohomology modules $H^i_{\mathfrak{m}}(R)$ have no embedded attached primes). We obtain some additional cases if $R/\mathfrak{m}$ is perfect or if $R$ is $\mathbb N$-graded.