F-stable secondary representations and deformation of F-injectivity

Abstract

We prove that deformation of F-injectivity holds for local rings $(R,\mathfrak{m})$ that admit secondary representations of $H_{\mathfrak{m}}^i(R)$ 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 $H_{\mathfrak{m}}^i(R)$ have no embedded attached primes). We obtain some additional cases if $R/\mathfrak{m}$ is perfect or if $R$ is $\mathbb{N}$-graded.

9 pages. Minor changes from previous version

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