{
  "abstract": "Let $(V,q)$ be an anisotropic quadratic space of dimension $4$ over the rationals and let $p$ be a prime such that the local quadratic space $V\\otimes \\mathbb{Q}_p$ is the orthogonal direct sum of two hyperbolic planes. We show that the group of $p$-adic rigid meromorphic cocycles attached to $V$ has infinite rank. A key ingredient in the proof is the computation of the group of invertible rigid analytic functions on products of certain rigid analytic subspaces of the projective line such as the $p$-adic upper half-plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24309",
  "author_total": 2,
  "authors": [
    {
      "name": "Lennart Gehrmann"
    },
    {
      "name": "Sören Sprehe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dsgnq27vn047z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24309",
  "fulltext_url": null,
  "id": "dsgnq27vn047z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24309",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214049959",
  "pdf_url": "https://arxiv.org/pdf/2609.24309",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dsgnq27vn047z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24309",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24309"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the abundance of rigid meromorphic cocycles for quadratic forms in four variables",
  "title_text": "On the abundance of rigid meromorphic cocycles for quadratic forms in four variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dsgnq27vn047z",
  "venue": "arXiv",
  "versions": []
}