{
  "id": "1306.3251",
  "version": "v3",
  "published": "2013-06-13T20:30:27.000Z",
  "updated": "2014-10-08T20:51:29.000Z",
  "title": "On Brauer groups of double covers of ruled surfaces",
  "authors": [
    "Brendan Creutz",
    "Bianca Viray"
  ],
  "comment": "v3: Sections 4-6 expanded/rewritten",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with generators given by central simple algebras over the function field of X and relations coming from the N\\'eron-Severi group of X. In particular, the result gives a central simple algebra representative for the unique nontrivial Brauer class on any Enriques surface. An example demonstrating the applications to the study of rational points is given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-13T03:28:22.000Z",
      "comment": "v2: This version replaces Part II of v1. Part I of v1 is now available as arXiv:14032924",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-08T20:51:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14G05"
    ],
    "keywords": [
      "brauer group",
      "ruled surface",
      "unique nontrivial brauer class",
      "main result",
      "function field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3251C"
    }
  }
}