{
  "id": "1802.09489",
  "version": "v1",
  "published": "2018-02-26T18:11:36.000Z",
  "updated": "2018-02-26T18:11:36.000Z",
  "title": "Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series",
  "authors": [
    "Jan Hendrik Bruinier",
    "Tonghai Yang"
  ],
  "comment": "59 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let V be a rational quadratic space of signature (m,2). A conjecture of Kudla relates the arithmetic degrees of top degree special cycles on an integral model of a Shimura variety associated with SO(V) to the coefficients of the central derivative of an incoherent Siegel Eisenstein series of genus m+1. We prove this conjecture for the coefficients of non-singular index T when T is not positive definite. We also prove it when T is positive definite and the corresponding special cycle has dimension 0. To obtain these results, we establish new local arithmetic Siegel-Weil formulas at the archimedean and non-archimedian places.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-26T18:11:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35",
      "14G40",
      "11G18",
      "11F27"
    ],
    "keywords": [
      "arithmetic degrees",
      "incoherent siegel eisenstein series",
      "local arithmetic siegel-weil formulas",
      "derivative",
      "positive definite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}