{
  "id": "0810.5760",
  "version": "v1",
  "published": "2008-10-31T19:02:57.000Z",
  "updated": "2008-10-31T19:02:57.000Z",
  "title": "Period and index of genus one curves over number fields",
  "authors": [
    "Shahed Sharif"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over certain number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-31T19:02:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05"
    ],
    "keywords": [
      "number fields",
      "smallest positive degree",
      "galois-invariant divisor classes",
      "rational divisors",
      "construct examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.5760S"
    }
  }
}