{
  "abstract": "We prove that, for every non-uniform arithmetic lattice in $\\mathrm{SU}(2,1)$, its inverse images in the universal cover and in all connected finite covers are residually finite. The key new input is that every commensurability class of such lattices contains a congruence arithmetic lattice $Γ$ for which $$H^1_{\\mathrm{cusp}}(Γ\\backslash\\mathbb B^2,\\mathbb C)\\ne 0.$$ In particular, the first inner cohomology of this ball quotient is non-zero. The proof uses Rogawski's endoscopic classification for $\\mathrm{U}(3)$. A cohomological criterion proved previously by the author then gives the residual-finiteness result. Residual finiteness also yields multiplier systems of arbitrary denominator on suitable finite-index subgroups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07639",
  "author_total": 1,
  "authors": [
    {
      "name": "Richard M. Hill"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d09c1fpkzsqt3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07639",
  "fulltext_url": null,
  "id": "d09c1fpkzsqt3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07639",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212075004",
  "pdf_url": "https://arxiv.org/pdf/2609.07639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d09c1fpkzsqt3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07639"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Residual finiteness and cuspidal cohomology of Picard modular surfaces",
  "title_text": "Residual finiteness and cuspidal cohomology of Picard modular surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/d09c1fpkzsqt3",
  "venue": "arXiv",
  "versions": []
}