{
  "id": "0802.4016",
  "version": "v1",
  "published": "2008-02-27T13:17:19.000Z",
  "updated": "2008-02-27T13:17:19.000Z",
  "title": "Rational points in periodic analytic sets and the Manin-Mumford conjecture",
  "authors": [
    "Jonathan Pila",
    "Umberto Zannier"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to view torsion points as rational points on a complex torus and then compare (i) upper bounds for the number of rational points on a transcendental analytic variety (Bombieri-Pila-Wilkie) and (ii) lower bounds for the degree of a torsion point (Masser), after taking conjugates. In order to be able to deal with (i), we discuss (Thm. 2.1) the semi-algebraic curves contained in an analytic variety supposed invariant for translations by a full lattice, which is a topic with some independent motivation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-27T13:17:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational points",
      "periodic analytic sets",
      "manin-mumford conjecture",
      "analytic variety supposed invariant",
      "view torsion points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.4016P"
    }
  }
}