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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关于局部上同调的相关质数

让$R$是素特征的可交换诺特环$p$. 在本文中，我们使用过滤规则序列给出了一个简短的证明，即$H_{I}^{t}(R)$对于任何理想都是有限的$I$并且对于任何$t\geqslant 0$什么时候$R$有有限的$F$-表示类型或有限奇异轨迹。这扩展了 Takagi–Takahashi 先前的结果，并在许多新的正特征环类中对 Huneke 问题给出了肯定的答案。我们还给出了一个关于奇点的标准$R$（在任何特征中）以保证集合$\operatorname{Ass}H_{I}^{2}(R)$总是有限的。