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  • HAILONG DAO (a1) and PHAM HUNG QUY (a2)


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.



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This paper was done while the second author was visiting Vietnam Institute for Advanced Study in Mathematics.



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  • HAILONG DAO (a1) and PHAM HUNG QUY (a2)


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