{
  "id": "1009.4306",
  "version": "v1",
  "published": "2010-09-22T09:31:20.000Z",
  "updated": "2010-09-22T09:31:20.000Z",
  "title": "Density of rational points on elliptic surfaces",
  "authors": [
    "Ronald van Luijk"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V, not equal to V, such that for each field extension K of k of degree at most d over the field of rational numbers, the set V(K) is Zariski dense as soon as it contains any point outside Z. We also present a version of this statement that is universal over certain twists of V and over all extensions of k. This generalizes a result of Swinnerton-Dyer, as well as previous work of Logan, McKinnon, and the author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-22T09:31:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic surfaces",
      "rational points",
      "field extension",
      "number field",
      "rational numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4306V"
    }
  }
}