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arXiv · 2606.07518

On Hellus--Lyubeznik--Yildirim's conjecture of local cohomology modules

Alberto F. Boix·Majid Eghbali
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Abstract

The goal of this paper is to study the so--called Hellus--Lyubeznik--Yildirim (HLY) conjecture, that predicts the following: given a regular local ring $(R,\mathfrak{m})$, and any ideal $I\subset R$, zero is an associated prime ideal of the Matlis dual of any non--zero local cohomology module supported on $I$. Among other results, we give some partial positive answers to this conjecture in the following cases: when $\operatorname{depth} (R/I)=1$, when $\operatorname{depth} (R/I)=2$ under some extra assumptions, when $I$ is a squarefree monomial ideal inside a formal power series ring over a field, and when $R$ is a formal power series over a discrete valuation ring of mixed characteristic.

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Alberto F. Boix, Majid Eghbali. 2026-04-07. On Hellus--Lyubeznik--Yildirim's conjecture of local cohomology modules. https://arxiv.org/abs/2606.07518

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