{
  "id": "0712.1782",
  "version": "v1",
  "published": "2007-12-11T17:50:46.000Z",
  "updated": "2007-12-11T17:50:46.000Z",
  "title": "Existence of rational points on smooth projective varieties",
  "authors": [
    "Bjorn Poonen"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Fix a number field k. We prove that if there is an algorithm for deciding whether a smooth projective geometrically integral k-variety has a k-point, then there is an algorithm for deciding whether an arbitrary k-variety has a k-point and also an algorithm for computing X(k) for any k-variety X for which X(k) is finite. The proof involves the construction of a one-parameter algebraic family of Chatelet surfaces such that exactly one of the surfaces fails to have a k-point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-11T17:50:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G35",
      "11U05",
      "14G25",
      "14J20"
    ],
    "keywords": [
      "smooth projective varieties",
      "rational points",
      "smooth projective geometrically integral k-variety",
      "number field",
      "arbitrary k-variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1782P"
    }
  }
}