{
  "abstract": "Let $\\mathbb{F}_q$ be a finite field with $q = p^s$ elements. Let $S = \\bigoplus_{n \\geq 0} S_n$ be a non-negatively graded commutative, Noetherian $\\mathbb{F}_q$-algebra. Assume $S$ has a structure of an unstable Steenrod algebra. Let $M$ be a finitely generated graded unstable $S$-module. Let $I$ be a homogeneous ideal in $S$. We prove that for $i \\geq 0$ the local cohomology modules $H^i_I(M)$ has a structure of a Cartan $S$-module. As application we give a direct and considerably simpler proof of D. Bourguiba and S. Zarati's generalization of Landweber-Stong conjecture. We also give a necessary and sufficient condition for $S$ to have $S_r$-property of Serre in terms of Dickson polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08531",
  "author_total": 1,
  "authors": [
    {
      "name": "Tony J. Puthenpurakal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7b7y58w5qrgq8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08531",
  "fulltext_url": null,
  "id": "7b7y58w5qrgq8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08531",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7b7y58w5qrgq8.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local cohomology over Steenrod algebras",
  "title_text": "Local cohomology over Steenrod algebras",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/7b7y58w5qrgq8",
  "venue": "arXiv",
  "versions": []
}