{
  "abstract": "Let $G$ be a semisimple Lie group that is not isogenous to the isometry group of real or complex hyperbolic $n$-space. We show that the rational rank is a profinite invariant for irreducible lattices in $G$, unless $G$ has type $D_{2n}$ which forms a genuine exception. In particular, profinitely isomorphic lattices in $G$ of type $D_{2n}$ can have differing virtual cohomological dimension. As another corollary, uniformity is a profinite property for irreducible lattices in $G$ outside type $D_4$. Assuming CSP, the existence of triality symmetries gives uniform and non-uniform profinitely isomorphic lattices in type $D_4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17041",
  "author_total": 1,
  "authors": [
    {
      "name": "Holger Kammeyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w5x6b3398v0d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17041",
  "fulltext_url": null,
  "id": "3w5x6b3398v0d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17041",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221763481",
  "pdf_url": "https://arxiv.org/pdf/2610.17041",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w5x6b3398v0d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17041",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17041"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Profinite recognition of uniformity",
  "title_text": "Profinite recognition of uniformity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/3w5x6b3398v0d",
  "venue": "arXiv",
  "versions": []
}