{
  "abstract": "Let $R$ be a commutative Noetherian ring, let $\\mathbf{x}=x_1,\\ldots,x_n$ be an $R$-regular sequence, and let $\\mathbf{y}=y_1,\\ldots,y_m$ be a sequence of elements of $R$. Put $I=(\\mathbf y)$. Let $\\mathcal S$ be a Serre subcategory of the category of $R$-modules. We consider the double complex obtained from the Koszul co-complex with respect to $\\mathbf x$ and the Čech complex with respect to $\\mathbf y$. Using the two spectral sequences associated with this double complex, we prove that \\[ Ext_R^i(R/(\\mathbf x),H_I^j(R))\\in\\mathcal S \\quad\\text{for all }i,j\\in \\mathbb N_0 \\] implies \\[ H_I^j(R/(\\mathbf x))\\in\\mathcal S \\quad\\text{for all }j\\in\\mathbb N_0. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20171",
  "author_total": 1,
  "authors": [
    {
      "name": "Maryam Jahangiri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vgda8079f88w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20171",
  "fulltext_url": null,
  "id": "8vgda8079f88w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20171",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7203869276",
  "pdf_url": "https://arxiv.org/pdf/2608.20171",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vgda8079f88w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2608.20171",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20171"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Koszul cohomology of Čech cohomology modules",
  "title_text": "Koszul cohomology of Čech cohomology modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8vgda8079f88w",
  "venue": "arXiv",
  "versions": []
}