{
  "abstract": "The new framework of semi-tautological extensions has allowed for explicit understanding of low-degree odd cohomology groups of moduli spaces of stable curves. Let $S^*_ω(\\overline{\\mathcal M}_{g,n}) \\subset H^*(\\overline{\\mathcal M}_{g,n})$ denote the semi-tautological extension generated by $H^{11}(\\overline{\\mathcal M}_{1,11})$, that is, the smallest system of subrings of $H^*(\\overline{\\mathcal M}_{g,n})$ containing $H^{11}(\\overline{\\mathcal M}_{1,11})$ and the tautological subrings, which is also closed under pullbacks along forgetful maps and pushforwards along gluing maps. Recently, it has been shown that $H^{11}(\\overline{\\mathcal M}_{g,n}) = S^{11}_ω(\\overline{\\mathcal M}_{g,n})$ and $H^{13}(\\overline{\\mathcal M}_{g,n}) = S^{13}_ω(\\overline{\\mathcal M}_{g,n})$ for all $g$ and $n$. Meanwhile, $H^{15}(\\overline{\\mathcal M}_{1,n}) \\neq S_ω^{15}(\\overline{\\mathcal M}_{1,n})$ for all $n \\geq 15$. Nevertheless, we prove that $H^{15}(\\overline{\\mathcal M}_{2,n}) = S^{15}_ω(\\overline{\\mathcal M}_{2,n})$ for all $n$. Moreover, we determine all relations in $S_ω^{15}(\\overline{\\mathcal M}_{g,n})$ for all $g \\geq 2$ and give explicit bases for this vector space in terms of decorated graphs. Conditional upon the conjectured dimension of $H^{15}(\\overline{\\mathcal M}_{3,14})$, we also prove that $H^{15}(\\overline{\\mathcal M}_{3,n}) = S^{15}_ω(\\overline{\\mathcal M}_{3,n})$ for all $n$. As an application, we prove $H^*(\\overline{\\mathcal M}_{g,n}) = RH^*(\\overline{\\mathcal M}_{g,n})$ for several new small pairs $(g,n)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14377",
  "author_total": 4,
  "authors": [
    {
      "name": "Amy Bradford"
    },
    {
      "name": "Aitor Iribar López"
    },
    {
      "name": "Andreas Kretschmer"
    },
    {
      "name": "Hannah Larson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0p8w50pwf1hmk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14377",
  "fulltext_url": null,
  "id": "0p8w50pwf1hmk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14377",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221765771",
  "pdf_url": "https://arxiv.org/pdf/2610.14377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0p8w50pwf1hmk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14377"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The fifteenth cohomology group of moduli spaces of stable curves",
  "title_text": "The fifteenth cohomology group of moduli spaces of stable curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0p8w50pwf1hmk",
  "venue": "arXiv",
  "versions": []
}