{
  "id": "1708.01192",
  "version": "v1",
  "published": "2017-08-03T16:13:08.000Z",
  "updated": "2017-08-03T16:13:08.000Z",
  "title": "The rational points on certain Abelian varieties over function fields",
  "authors": [
    "Sajad Salami"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a structure theorem on the Mordell-Weil group of Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of quasi-projective varieties, in terms of Prym varieties associated to the cyclic covers. Given integers $2\\leq s \\leq r$ and a polynomial $f(x)$ of degree $r$ with coefficients in a global field, we apply our result to the twists of Jacobian varieties of super-elliptic curves defined by affine equation $y^s=f(x)$ with cyclic covers of certain varieties to get super-elliptic Jacobians with large Mordell-Weil ranks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T16:13:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian varieties",
      "function fields",
      "rational points",
      "cyclic covers",
      "large mordell-weil ranks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}