{
  "id": "0712.1785",
  "version": "v2",
  "published": "2007-12-11T17:56:01.000Z",
  "updated": "2007-12-18T15:18:57.000Z",
  "title": "The set of non-squares in a number field is diophantine",
  "authors": [
    "Bjorn Poonen"
  ],
  "comment": "5 pages; corrected minor typos, improved exposition, added reference",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Fix a number field k. We prove that k* - k*^2 is diophantine over k. This is deduced from a theorem that for a nonconstant separable polynomial P(x) in k[x], there are at most finitely many a in k* modulo squares such that there is a Brauer-Manin obstruction to the Hasse principle for the conic bundle X given by y^2 - az^2 = P(x).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-18T15:18:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G35",
      "11U99",
      "14G25",
      "14J20"
    ],
    "keywords": [
      "number field",
      "diophantine",
      "non-squares",
      "conic bundle",
      "modulo squares"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1785P"
    }
  }
}