{
  "id": "2207.09513",
  "version": "v1",
  "published": "2022-07-19T18:53:19.000Z",
  "updated": "2022-07-19T18:53:19.000Z",
  "title": "Integral canonical models for Shimura varieties defined by tori",
  "authors": [
    "Patrick Daniels"
  ],
  "comment": "29 pages. Comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove the Pappas-Rapoport conjecture on the existence of canonical integral models of Shimura varieties with parahoric level structure in the case where the Shimura variety is defined by a torus. As an important ingredient, we show, using the Bhatt-Scholze theory of prismatic $F$-crystals, that there is a fully faithful functor from $\\mathcal{G}$-valued crystalline representations of Gal$(\\bar{K}/K)$ to $\\mathcal{G}$-shtukas over Spd$(\\mathcal{O}_K)$, where $\\mathcal{G}$ is a parahoric group scheme over $\\mathbb{Z}_p$ and $\\mathcal{O}_K$ is the ring of integers in a $p$-adic field $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-19T18:53:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18"
    ],
    "keywords": [
      "shimura variety",
      "integral canonical models",
      "parahoric level structure",
      "parahoric group scheme",
      "pappas-rapoport conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}