On the associated primes of local cohomology

Abstract

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^ t_I (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 ...