{
  "id": "2011.12840",
  "version": "v1",
  "published": "2020-11-25T15:50:23.000Z",
  "updated": "2020-11-25T15:50:23.000Z",
  "title": "Hilbert's irreducibility theorem for abelian varieties",
  "authors": [
    "Pietro Corvaja",
    "Julian Lawrence Demeio",
    "Ariyan Javanpeykar",
    "Davide Lombardo",
    "Umberto Zannier"
  ],
  "comment": "37 pages. Comments more than welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove a version of Hilbert's irreducibility theorem for abelian varieties over finitely generated fields of characteristic zero, thereby generalizing earlier results of Zannier for powers of non-CM elliptic curves. Our work proves a conjecture of Corvaja-Zannier on varieties with many rational points in the case of abelian varieties, and confirms predictions made by Lang's conjecture on rational points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-25T15:50:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilberts irreducibility theorem",
      "abelian varieties",
      "rational points",
      "non-cm elliptic curves",
      "langs conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}