{
  "abstract": "We prove the norm principle for the extended Clifford group $Ω(q)$ of every nondegenerate quadratic form $q$ of even dimension at least $4$ over an arbitrary field $F$ of characteristic different from $2$, for all finite separable field extensions $L/F$. The main new ingredient is a factorization theorem for proper similitudes: for a quadratic extension $L/F$ and $f\\in \\mathrm{GO}^+(q)(L)$, there exist $u\\in \\mathrm{SO}(q)(L)$, a maximal $F$-torus $S\\subset \\mathrm{GO}^+(q)$, and $s\\in S(L)$ such that $f=us$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30607",
  "author_total": 1,
  "authors": [
    {
      "name": "Federico Scavia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mqj022jd7zfb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30607",
  "fulltext_url": null,
  "id": "0mqj022jd7zfb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30607",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214684912",
  "pdf_url": "https://arxiv.org/pdf/2609.30607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mqj022jd7zfb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The norm principle for extended Clifford groups",
  "title_text": "The norm principle for extended Clifford groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/0mqj022jd7zfb",
  "venue": "arXiv",
  "versions": []
}