On the associated primes of local cohomology

Abstract

Let $R$ be a commutative Noetherian ring of prime characteristic $p$. In this paper we give a short proof using filter regular sequences that the set of associated prime ideals of $H_I^t(R)$ is finite for any ideal $I$ and for any $t\ge 0$ when $R$ has finite $F$-representation type or finite singular locus. This extends a previous result by Takagi-Takahashi and gives affirmative answers for a problem of Huneke in many new classes of rings in positive characteristic. We also give a criterion about the singularities of $R$ (in any characteristic) to guarantee that the set of associated primes of $H_I^2(R)$ is always finite.

We added Remark 1.1 about the work of Mel Hochster and Luis Núñez-Betancourt, who obtained the same result as our main Theorem. Also, Corollary 3.4 was added

References in corpus (2)

• Depth of $F$-singularities and base change of relative canonical sheaves
• $F$-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic $p>0$

Cited by in corpus (1)

• FFRT Properties of hypersurfaces and their F-signature