{
  "abstract": "For a simplicial poset $P$, Stanley assigned the face ring $A_P$, which is the quotient of the polynomial ring $S:=K[t_x \\mid x \\in P \\setminus \\{\\widehat{0} \\}]$ by the ideal $I_P$. This is a generalization of Stanley-Reisner rings, but the grading of $S$ is more involved. Building on our previous paper, we further develop and complete the study of the local cohomology modules $H_{I_P}^i(S)$. In our categorical framework, $\\mathrm{Ext}_S(A_P, S)$ ``encodes\" all the information of $H_{I_P}^i(S)$. We treat $H_{I_P}^i(S)$ in a reasonably explicit way. In particular, Lyubeznik numbers $λ_{i,j}(A_P)$ can be simply expressed in terms of $[\\mathrm{Ext}_S^*(\\mathrm{Ext}_S^*(A_P,S), S)]_\\bf{0}$, and depend only on the homeomorphism class of the underlying space of the CW complex associated with $P$ and $\\mathrm{char}(K)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38478",
  "author_total": 2,
  "authors": [
    {
      "name": "Kosuke Shibata"
    },
    {
      "name": "Kohji Yanagawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54vx5aq8dn52f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38478",
  "fulltext_url": null,
  "id": "54vx5aq8dn52f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38478",
  "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/2610.38478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54vx5aq8dn52f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lyubeznik numbers of the face rings of simplicial posets",
  "title_text": "Lyubeznik numbers of the face rings of simplicial posets",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/54vx5aq8dn52f",
  "venue": "arXiv",
  "versions": []
}