{
  "abstract": "The determinant approximation conjecture states that for a residually finite group $G$ and a chain $G_i$ of finite index normal subgroups with trivial intersection, the Fuglede-Kadison determinant of every matrix over the group algebra $\\mathbb{Q} G$ is the limit of the Fuglede-Kadison determinants of the matrix reductions from $\\mathbb{Q} G$ to $\\mathbb{Q} (G/G_i)$. We disprove the conjecture by exhibiting an explicit element of the integral group ring of the Heisenberg group with determinant equal to $2$ and reduced determinants bounded by $\\sqrt[3]{5}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15567",
  "author_total": 1,
  "authors": [
    {
      "name": "Holger Kammeyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0z7knqyb1r96k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15567",
  "fulltext_url": null,
  "id": "0z7knqyb1r96k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15567",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213305604",
  "pdf_url": "https://arxiv.org/pdf/2609.15567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0z7knqyb1r96k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A counterexample to the determinant approximation conjecture",
  "title_text": "A counterexample to the determinant approximation conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0z7knqyb1r96k",
  "venue": "arXiv",
  "versions": []
}