{
  "abstract": "Over $\\mathbb C$, we compute the integral Chow ring of $\\mathcal A_3$, the moduli stack of principally polarized abelian threefolds. Along the way, we compute the integral Chow ring of $\\mathcal M_3$, the moduli stack of smooth genus-three curves. The ring $\\CH(\\mathcal A_3)$ is generated by the Chern classes of the Hodge bundle, along with three classes supported on the locus of decomposable abelian varieties, subject to 16 relations. The ring $\\CH(\\mathcal M_3)$ is generated by the Chern classes of the Hodge bundle, with five relations. In particular, we find that the top Chern class of the Hodge bundle, $λ_3$, has order 504 on $\\mathcal A_3$ and 252 on $\\mathcal M_3$. For $\\mathcal A_3$, this removes the factor of 4 from the bound $252\\mid\\operatorname{ord}(λ_3)\\mid 1008$ of Ekedahl and van der Geer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06014",
  "author_total": 1,
  "authors": [
    {
      "name": "Emma Bishop"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cw4ms4zd3mkrt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06014",
  "fulltext_url": null,
  "id": "cw4ms4zd3mkrt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06014",
  "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.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cw4ms4zd3mkrt.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The integral Chow rings of $\\mathcal A_3$ and $\\mathcal M_3$",
  "title_text": "The integral Chow rings of 𝒜_3 and ℳ_3",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/cw4ms4zd3mkrt",
  "venue": "arXiv",
  "versions": []
}