On the factorial case of Huneke's conjecture for local cohomology modules

André Dosea; Cleto B. Miranda-Neto

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arXiv · 2405.06862

On the factorial case of Huneke's conjecture for local cohomology modules

André Dosea·Cleto B. Miranda-Neto

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Abstract

A conjecture raised in 1990 by C. Huneke predicts that, for a $d$-dimensional Noetherian local ring $R$, local cohomology modules of finitely generated $R$-modules have finitely many associated primes. Although counterexamples do exist, the conjecture has been confirmed in several cases, for instance if $d\leq 3$, and witnessed some progress in special cases for higher $d$. In this paper, assuming that $R$ is a factorial domain, we establish the case $d=4$, and under different additional conditions (in a couple of results) also the case $d=5$. Finally, when $R$ is regular and contains a field, we apply the Hartshorne-Lichtenbaum vanishing theorem as a tool to deal with the case $d=6$.

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André Dosea, Cleto B. Miranda-Neto. 2024-05-11. On the factorial case of Huneke's conjecture for local cohomology modules. https://arxiv.org/abs/2405.06862

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