{
  "abstract": "We prove the finiteness of the genus of quaternion division algebras over some formally real fields. In particular, if $F$ is a formally real field and the second power of the fundamental ideal $I^2(F)$ is torsion-free, then the genus of any quaternion division $F$-algebra is trivial. For instance, this immediately implies that the genus vanishes for any quaternion division algebra over a formally real pythagorean field. The proofs are based on methods from the theory of quadratic forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05392",
  "author_total": 1,
  "authors": [
    {
      "name": "Sergey V. Tikhonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c2sjemdsb3cn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05392",
  "fulltext_url": null,
  "id": "5c2sjemdsb3cn",
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  "landing_url": "https://arxiv.org/abs/2610.05392",
  "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.RA"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220707345",
  "pdf_url": "https://arxiv.org/pdf/2610.05392",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c2sjemdsb3cn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05392",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05392"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Genus of quaternion algebras over formally real fields",
  "title_text": "Genus of quaternion algebras over formally real fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/5c2sjemdsb3cn",
  "venue": "arXiv",
  "versions": []
}