{
  "id": "0807.0502",
  "version": "v1",
  "published": "2008-07-03T08:08:14.000Z",
  "updated": "2008-07-03T08:08:14.000Z",
  "title": "Faltings heights of CM cycles and derivatives of L-functions",
  "authors": [
    "Jan Hendrik Bruinier",
    "Tonghai Yang"
  ],
  "comment": "50 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the Faltings height pairing of arithmetic Heegner divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedian contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura variety has dimension 0, 1, or 2. In particular, we obtain a new proof of the Gross-Zagier formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-03T08:08:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G40",
      "11F67"
    ],
    "keywords": [
      "cm cycles",
      "faltings height",
      "shimura variety",
      "arithmetic heegner divisors",
      "derivative"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0502H"
    }
  }
}