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arXiv · 2506.17586

Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings

Ryotaro Hanyu
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Abstract

We investigate the finiteness of the set of associated primes for local cohomology modules $H_I^{i}(J)$ of an ideal $J$ generated by an $R$-sequence, through the comparison of $H_I^{d+1}(J)$ and $H_I^d(R/J)$, where $d = \mathrm{depth}_I(R)$. The properties of almost factorial rings play a key role in enabling this comparison. Under suitable conditions, we prove that the finiteness of $\mathrm{Ass} H_I^{d+1}(J)$ is equivalent to that of $\mathrm{Ass} H_I^d(R/J)$. Moreover, we give a few conditions under which the finiteness of $\mathrm{Ass} H_I^i(J)$ holds for all $i$.

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Ryotaro Hanyu. 2025-06-21. Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings. https://arxiv.org/abs/2506.17586

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