{
  "id": "math/9906156",
  "version": "v2",
  "published": "1999-06-23T13:52:13.000Z",
  "updated": "2000-11-06T18:15:40.000Z",
  "title": "On certain uniformity properties of curves over function fileds",
  "authors": [
    "Lucia Caporaso"
  ],
  "comment": "Improved exposition, added references, to appear on Comp. Math",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let g be an integer greater than 1. A uniform version of the Parshin-Arakelov theorem on the finiteness of the set of non-isotrivial curves of genus g over a function field, with fixed degeneracy locus, is proved. This is applied to obtain a uniform version of Manin theorem (the Mordell conjecture on rational points for curves of genus g over function fields). By a \"function field\" is meant the function field of a complex variety V of any dimension. If V is a curve, the uniform bounds will depend on g, on the genus of V and on the cardinality of the degeneracy locus.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-11-06T18:15:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Dxx"
    ],
    "keywords": [
      "function field",
      "function fileds",
      "uniformity properties",
      "uniform version",
      "parshin-arakelov theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6156C"
    }
  }
}