{
  "id": "0911.1271",
  "version": "v2",
  "published": "2009-11-06T15:16:21.000Z",
  "updated": "2012-03-27T13:27:07.000Z",
  "title": "Local heights on Galois covers of the projective line",
  "authors": [
    "Robin de Jong"
  ],
  "comment": "18 pages",
  "journal": "Acta Arithmetica 152 (2012), 51--70",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let X be a smooth projective curve of positive genus defined over a number field K. Assume given a Galois covering map x from X to the projective line over K and a place v of K. We introduce a local canonical height on the set of K_v-valued points of X associated to x as an integral with logarithmic integrand, generalizing Tate's local Neron function on an elliptic curve. The resulting global height can be viewed as a 'Mahler measure' associated to x. We prove that the local canonical height can be obtained by averaging, and taking a limit, over divisors of higher order Weierstrass points on X. This generalizes previous results by Everest-ni Fhlathuin and Szpiro-Tucker. Our construction of the local canonical height is an application of potential theory on Berkovich curves in the presence of a canonical measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-27T13:27:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G30",
      "11G50"
    ],
    "keywords": [
      "projective line",
      "galois covers",
      "local canonical height",
      "local heights",
      "higher order weierstrass points"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.1271D"
    }
  }
}