{
  "id": "0705.4324",
  "version": "v1",
  "published": "2007-05-30T01:10:34.000Z",
  "updated": "2007-05-30T01:10:34.000Z",
  "title": "Rings of Algebraic Numbers in Infinite Extensions of $\\Q$ and Elliptic Curves Retaining Their Rank",
  "authors": [
    "Alexandra Shlapentokh"
  ],
  "categories": [
    "math.NT",
    "math.LO"
  ],
  "abstract": "We show that elliptic curves whose Mordell-Weil groups are finitely generated over some infinite extensions of $\\Q$, can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite extensions of rational numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-30T01:10:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11U05",
      "11G05"
    ],
    "keywords": [
      "infinite extensions",
      "elliptic curves retaining",
      "algebraic numbers",
      "rational numbers",
      "mordell-weil groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.4324S"
    }
  }
}