{
  "id": "1708.05820",
  "version": "v1",
  "published": "2017-08-19T07:49:35.000Z",
  "updated": "2017-08-19T07:49:35.000Z",
  "title": "Heights of CM cycles and derivatives of L-series",
  "authors": [
    "Yara Elias",
    "Tian An Wong"
  ],
  "comment": "39 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier formula for modular forms of even weight in terms of an arithmetic intersection pairing of CM-cycles on Kuga-Sato varieties over Shimura curves. Combined with a result of the first author and de Vera-Piquero adapting Kolyvagin's method of Euler systems to this setting, we bound the associated Selmer and Tate-Shafarevich groups, assuming the non-vanishing of the derivative of the L-function at the central point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-19T07:49:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F12",
      "11F85"
    ],
    "keywords": [
      "cm cycles",
      "vera-piquero adapting kolyvagins method",
      "derivative",
      "kuga-sato varieties",
      "shimura curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}