On the associated primes of local cohomology

Hailong Dao; Pham Hung Quy

On the associated primes of local cohomology

Commutative Algebra 2016-03-01 v2

Authors: Hailong Dao , Pham Hung Quy

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 any characteristic) to guarantee that the set of associated primes of $H^2_I(R)$ is always finite.

Keywords

local cohomology associated primes commutative noetherian ring filter regular sequence F-representation type singular locus positive characteristic

Cite

@article{arxiv.1602.00421,
  title  = {On the associated primes of local cohomology},
  author = {Hailong Dao and Pham Hung Quy},
  journal= {arXiv preprint arXiv:1602.00421},
  year   = {2016}
}

Comments

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

On the associated primes of local cohomology

Abstract

Keywords

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