{
  "id": "1301.1226",
  "version": "v3",
  "published": "2013-01-07T15:22:53.000Z",
  "updated": "2013-10-19T08:29:14.000Z",
  "title": "The supersingular locus of the Shimura variety for GU(1,n-1) over a ramified prime",
  "authors": [
    "Michael Rapoport",
    "Ulrich Terstiege",
    "Sean Wilson"
  ],
  "comment": "A few more corrections, to appear in Math. Zeitschrift",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We analyze the geometry of the supersingular locus of the reduction modulo p of a Shimura variety associated to a unitary similitude group GU(1,n-1) over Q, in the case that p is ramified. We define a stratification of this locus and show that its incidence complex is closely related to a certain Bruhat-Tits simplicial complex. Each stratum is isomorphic to a Deligne-Lusztig variety associated to some symplectic group over F_p and some Coxeter element. The closure of each stratum is a normal projective variety with at most isolated singularities. The results are analogous to those of Vollaard/Wedhorn in the case when p is inert.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-19T08:29:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35"
    ],
    "keywords": [
      "shimura variety",
      "supersingular locus",
      "ramified prime",
      "unitary similitude group gu",
      "bruhat-tits simplicial complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1226R"
    }
  }
}