{
  "abstract": "Let X be a smooth, projective, geometrically integral variety over a global function field k of characteristic p. We show that if the unipotent Brauer group of X is zero, and the Picard scheme of X is torsion free, then only finitely many places of k can be potentially relevant to the Brauer--Manin obstruction for X. In the opposite case, almost all places of k are potentially relevant. If X is base changed from a finite field, then in both cases the finite set of exceptional places is empty. We give an example of a supersingular K3 surface over a global function field k of characteristic p>2 such that Br(X) is finite modulo Br(k), answering a question from our previous paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.14967",
  "author_total": 2,
  "authors": [
    {
      "name": "Christopher D. Lazda"
    },
    {
      "name": "Alexei N. Skorobogatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6acpzx2s3d7pt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.14967",
  "fulltext_url": null,
  "id": "6acpzx2s3d7pt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.14967",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7164893127",
  "pdf_url": "https://arxiv.org/pdf/2606.14967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6acpzx2s3d7pt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.14967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.14967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Dichotomy for the Brauer-Manin obstruction in characteristic p",
  "title_text": "Dichotomy for the Brauer-Manin obstruction in characteristic p",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/6acpzx2s3d7pt",
  "venue": "arXiv",
  "versions": []
}