{
  "id": "2106.11337",
  "version": "v1",
  "published": "2021-06-21T18:10:12.000Z",
  "updated": "2021-06-21T18:10:12.000Z",
  "title": "Divisibility of polynomials and degeneracy of integral points",
  "authors": [
    "Erwan Rousseau",
    "Julie Tzu-Yueh Wang",
    "Amos Turchet"
  ],
  "comment": "26 pages. Comments welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties that are pseudo-arithmetically hyperbolic. This generalizes results of Corvaja and Zannier obtained in dimension 2 to arbitrary dimension. The key input is an application of the Ru-Vojta's strategy. We also obtain the analogue results for function fields and Nevanlinna theory with the goal to apply them in a future paper in the context of Campana's conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-21T18:10:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J87",
      "11J97",
      "14G05",
      "32A22"
    ],
    "keywords": [
      "integral points",
      "divisibility",
      "degeneracy",
      "polynomials",
      "campanas conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}