{
  "id": "2403.10653",
  "version": "v1",
  "published": "2024-03-15T19:39:31.000Z",
  "updated": "2024-03-15T19:39:31.000Z",
  "title": "On the Piatetski-Shapiro construction for integral models of Shimura varieties",
  "authors": [
    "Pol van Hoften",
    "Jack Sempliner"
  ],
  "comment": "63 pages, comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the Piatetski-Shapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois group Gamma of F acts on (H,Y), and we show that the Gamma-fixed points of the Shimura varieties for (H,Y) recover the Shimura varieties for (G,X) under some hypotheses. For Shimura varieties of Hodge type with parahoric level, we show that the same is true for the p-adic integral models constructed by Pappas--Rapoport, if p is unramified in F. We also study the Gamma-fixed points of the Igusa stacks of Zhang for (H,Y) and prove optimal results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-15T19:39:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G35"
    ],
    "keywords": [
      "shimura varieties",
      "piatetski-shapiro construction",
      "shimura datum",
      "galois group gamma",
      "gamma-fixed points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}