{
  "id": "0804.0600",
  "version": "v2",
  "published": "2008-04-03T18:30:52.000Z",
  "updated": "2011-02-17T15:39:25.000Z",
  "title": "Special cycles on unitary Shimura varieties I. unramified local theory",
  "authors": [
    "Stephen Kudla",
    "Michael Rapoport"
  ],
  "comment": "In this new version, suggestions by B. Howard, U. Terstiege, and the referee for Inventiones are taken into account. Also a mistake in the statement of the conjecture at the end of the introduction, that was accidentally added in the galleys for the published version, has been removed",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "The supersingular locus in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n-1) over Q is uniformized by a formal scheme \\Cal N. In the case when p is inert, we define special cycles Z(x) in \\Cal N, associated to a collection x of m `special homomorphisms' with fundamental matrix T in Herm_m(OK). When m=n and T is nonsingular, we show that the cycle Z(x) is a union of components of the Ekedahl-Oort stratification, and we give a necessary and sufficient conditions, in terms of T, for Z(x) to be irreducible. When Z(x) is zero dimensional -- in which case it reduces to a single point -- we determine the length of the corresponding local ring by using a variant of the theory of quasi-canonical liftings. We show that this length coincides with the derivative of a representation density for hermitian forms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-17T15:39:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35"
    ],
    "keywords": [
      "unitary shimura varieties",
      "unramified local theory",
      "shimura variety",
      "unitary similitude group gu",
      "define special cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0600K"
    }
  }
}