{
  "id": "0912.3758",
  "version": "v2",
  "published": "2009-12-18T18:16:45.000Z",
  "updated": "2012-12-18T12:33:19.000Z",
  "title": "Special cycles on unitary Shimura varieties II: global theory",
  "authors": [
    "Stephen Kudla",
    "Michael Rapoport"
  ],
  "comment": "Material on occult period maps has been moved to a separate article. Various corrections and improvements in exposition have been made. Accepted for publication in Crelle",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n-1, 1). We define arithmetic cycles on these models and study their intersection behaviour. In particular, in the non-degenerate case, we prove a relation between their intersection numbers and Fourier coefficients of the derivative at s=0 of a certain incoherent Eisenstein series for the group U(n, n). This is done by relating the arithmetic cycles to their formal counterpart from Part I via non-archimedean uniformization, and by relating the Fourier coefficients to the derivatives of representation densities of hermitian forms. The result then follows from the main theorem of Part I and a counting argument.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-18T12:33:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35",
      "11F15",
      "11F18",
      "11F27"
    ],
    "keywords": [
      "unitary shimura varieties",
      "special cycles",
      "global theory",
      "fourier coefficients",
      "define arithmetic cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3758K"
    }
  }
}