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On the associated primes of local cohomology

Authors
  • Dao, Hailong
  • Quy, Pham Hung
Type
Preprint
Publication Date
Feb 28, 2016
Submission Date
Feb 01, 2016
Identifiers
arXiv ID: 1602.00421
Source
arXiv
License
Yellow
External links

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.

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