{
  "id": "math/0312359",
  "version": "v2",
  "published": "2003-12-18T13:41:48.000Z",
  "updated": "2004-09-06T11:34:14.000Z",
  "title": "On the Arakelov theory of elliptic curves",
  "authors": [
    "Robin de Jong"
  ],
  "comment": "17 pages. 2nd version; same main results as in v1, but with a section added on the average height of quotients of an elliptic curve",
  "journal": "l'Ens. Math. 51 (2005), 179--201",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces and a formula for the \"energy\" of an isogeny between Riemann surfaces of genus 1. The latter formula provides an answer to a question originally posed by Szpiro.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-09-06T11:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "14G40",
      "14H52",
      "14K02"
    ],
    "keywords": [
      "elliptic curves",
      "arakelov theory",
      "arakelov intersection theory",
      "elliptic arithmetic surfaces",
      "note contains"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12359D"
    }
  }
}