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.
F-Stable Secondary Representations and Deformation of F-Injectivity
De Stefani A.;
2021-01-01
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.
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