{
  "id": "2007.01275",
  "version": "v1",
  "published": "2020-07-02T17:33:49.000Z",
  "updated": "2020-07-02T17:33:49.000Z",
  "title": "Normalization in integral models of Shimura varieties of Hodge type",
  "authors": [
    "Yujie Xu"
  ],
  "comment": "33 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $(G,X)$ be a Shimura datum of Hodge type, and $\\mathscr{S}_K(G,X)$ its integral model with hyperspecial level structure. We prove that $\\mathscr{S}_K(G,X)$ admits a closed embedding, which is compatible with moduli interpretations, into the integral model $\\mathscr{S}_{K'}(\\mathrm{GSp},S^{\\pm})$ for a Siegel modular variety. In particular, the normalization step in the construction of $\\mathscr{S}_K(G,X)$ is redundant. In particular, our results apply to the earlier integral models constructed by Rapoport and Kottwitz, as those models agree with the Hodge type integral models for appropriately chosen Shimura data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-02T17:33:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "11G15",
      "14G35",
      "14K22"
    ],
    "keywords": [
      "shimura varieties",
      "normalization",
      "hodge type integral models",
      "shimura datum",
      "hyperspecial level structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}