{
  "id": "2108.03584",
  "version": "v1",
  "published": "2021-08-08T07:54:12.000Z",
  "updated": "2021-08-08T07:54:12.000Z",
  "title": "The supersingular locus of the Shimura variety of $\\mathrm{GU}(2,n-2)$",
  "authors": [
    "Maria Fox",
    "Naoki Imai"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\\mathrm{GU}(2,n-2)$. More concretely, we realize irreducible components of the supersingular locus as closed subschemes of flag schemes over Deligne--Lusztig varieties defined by explicit conditions. Moreover we study the intersections of the irreducible components. A stratification of Deligne--Lusztig varieties defined using a power of Frobenius action appears in the description of the intersections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-08T07:54:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14M15"
    ],
    "keywords": [
      "supersingular locus",
      "shimura variety",
      "deligne-lusztig varieties",
      "frobenius action appears",
      "inert prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}