{
  "abstract": "For every even Galois representation in a family of prime conductor $\\ell$, we prove that if $k \\in \\mathbb{Z}_{\\geq 1}$ is maximal such that \\[\\ell \\equiv 1 \\bmod 3^k\\] then the even mod $3$ deformation ring $R_S \\otimes_{\\mathbb{Z}_3} \\mathbb{F}_3$ of level $S=\\{\\ell,3\\}$ does not have a quotient isomorphic to $\\mathbb{F}_3[T]/(T^{2+3^{k-1}})$. As a corollary, we deduce that the global even deformation rings $R_S$ are finite and flat in the category of $\\mathbb{Z}_3$-modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17865",
  "author_total": 1,
  "authors": [
    {
      "name": "Peter Vang Uttenthal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azsj88pwgbgyg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17865",
  "fulltext_url": null,
  "id": "azsj88pwgbgyg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17865",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221797775",
  "pdf_url": "https://arxiv.org/pdf/2610.17865",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azsj88pwgbgyg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17865",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17865"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fine structure of even Galois deformation rings",
  "title_text": "Fine structure of even Galois deformation rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/azsj88pwgbgyg",
  "venue": "arXiv",
  "versions": []
}