{
  "id": "2403.01899",
  "version": "v2",
  "published": "2024-03-04T09:58:12.000Z",
  "updated": "2024-07-17T10:37:04.000Z",
  "title": "De Rham $F$-gauges and Shimura varieties",
  "authors": [
    "Xu Shen"
  ],
  "comment": "41 pages; a few corrections and improvements",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We study $F$-gauges for de Rham cohomology of smooth algebraic varieties in characteristic $p$. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl-Oort stratifications by constructing universal de Rham $F$-gauges with $G$-structure. We also study the cohomology of de Rham $F$-gauges on these varieties. In particular, in the PEL type case and when the weights of the flat automorphic vector bundles are $p$-small, we determine the $F$-gauge structure on their de Rham cohomology by the associated dual BGG complexes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-17T10:37:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G35"
    ],
    "keywords": [
      "shimura varieties",
      "rham cohomology",
      "flat automorphic vector bundles",
      "pel type case",
      "smooth algebraic varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}