{
  "abstract": "In this paper, we consider arbitrary regular local ring $S$ and an ideal $J\\subset S$ whose minimal primes are cohomologically complete intersection. Using the Mayer-Vietoris spectral sequence, in Section 2, we construct examples of local cohomology modules $H^i_J (S)$, whose set of associated primes is finite. As a special case we show that the set of associated primes $H^i_J (S)$ is finite when minimal primes of $J$ are part of a specific regular system of parameters and satisfy a `Dropping Condition'. In Section 3, we prove Theorem 2.3 along with its asssociated corollary in a more general setting, without the use of `Dropping Condition'. These examples of local cohomology modules include the cases whose associative primes also can contain prime number $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.10064",
  "author_total": 1,
  "authors": [
    {
      "name": "Rajsekhar Bhattacharyya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ascvmem63fcn6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.10064",
  "fulltext_url": null,
  "id": "ascvmem63fcn6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.10064",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.10064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ascvmem63fcn6.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:33Z",
      "native_id": "2611.10064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.10064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finiteness of local cohomology modules over arbitrary regular local rings",
  "title_text": "Finiteness of local cohomology modules over arbitrary regular local rings",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:33Z",
  "url": "https://research.draconitic.com/paper/ascvmem63fcn6",
  "venue": "arXiv",
  "versions": []
}