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ON THE ASSOCIATED PRIMES OF LOCAL COHOMOLOGY
Nagoya Mathematical Journal ( IF 0.638 ) Pub Date : 2018-02-05 , DOI: 10.1017/nmj.2017.44
HAILONG DAO; PHAM HUNG QUY

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 $t\geqslant 0$ 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 $\operatorname{Ass}H_{I}^{2}(R)$ is always finite.
更新日期:2020-02-06

 

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