{
  "id": "1608.01371",
  "version": "v1",
  "published": "2016-08-03T21:57:44.000Z",
  "updated": "2016-08-03T21:57:44.000Z",
  "title": "Local-global principles for Weil-Châtelet divisibility in positive characteristic",
  "authors": [
    "Brendan Creutz",
    "José Felipe Voloch"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend existing results characterizing Weil-Ch\\^atelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of Gonz\\'alez-Avil\\'es and Tan, we characterize when local-global divisibility holds in such contexts, providing examples showing that these results are optimal. We give an example of an elliptic curve over a global field of characteristic $2$ containing a rational point which is locally divisible by $8$, but is not divisible by $8$ as well as examples showing that the analogous local-global principle for divisibility in the Weil-Ch\\^atelet group can also fail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-03T21:57:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive characteristic",
      "weil-châtelet divisibility",
      "global field",
      "local-global divisibility holds",
      "locally trivial torsors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}