{
  "id": "math/9907018",
  "version": "v2",
  "published": "1999-07-02T14:51:37.000Z",
  "updated": "2001-06-08T20:18:15.000Z",
  "title": "Canonical heights on elliptic curves in characteristic p",
  "authors": [
    "Matthew A. Papanikolas"
  ],
  "comment": "14 pages; final version",
  "journal": "Compositio Math. 122 (2000), 299-313",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We define a new canonical height pairing on the rational points of elliptic curves over global function fields which takes values in the multiplicative group of a completion of the function field. This height serves as an analogue of both the classical Neron-Tate height and analytic p-adic heights. Our main result is that under some general hypotheses this pairing is non-degenerate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-06-08T20:18:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G07",
      "11R58",
      "14G25"
    ],
    "keywords": [
      "elliptic curves",
      "canonical height",
      "characteristic",
      "analytic p-adic heights",
      "global function fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7018P"
    }
  }
}