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

[2506.17586] Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Commutative Algebra arXiv:2506.17586 (math) [Submitted on 21 Jun 2025 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings Authors: Ryotaro Hanyu View a PDF of the paper titled Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings, by Ryotaro Hanyu View PDF HTML (experimental) 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 $i$. Comments: 12 pages Subjects: Commutative Algebra (math.AC) MSC classes: 13D45, 13A15, 13F05 Cite as: arXiv:2506.17586 [math.AC] (or arXiv:2506.17586v3 [math.AC] for this version) https://doi.org/10.48550/arXiv.2506.17586 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ryotaro Hanyu [ view email ] [v1] Sat, 21 Jun 2025 04:54:38 UTC (13 KB) [v2] Wed, 6 Aug 2025 05:14:31 UTC (13 KB) [v3] Tue, 14 Apr 2026 04:30:23 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings, by Ryotaro Hanyu View PDF HTML (experimental) TeX Source view license Current browse context: math.AC < prev | next > new | recent | 2025-06 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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