{
  "id": "2409.11720",
  "version": "v1",
  "published": "2024-09-18T06:08:00.000Z",
  "updated": "2024-09-18T06:08:00.000Z",
  "title": "Systems of Hecke eigenvalues on subschemes of Shimura varieties",
  "authors": [
    "Stefan Reppen"
  ],
  "comment": "13 pages. Comments are welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that the systems of Hecke eigenvalues that appear in the coherent cohomology with coefficients in automorphic line bundles of any mod $p$ abelian type compact Shimura variety at hyperspecial level are the same as those appearing in any Hecke-equivariant closed subscheme. We also prove analogous results for noncompact Shimura varieties or nonclosed subschemes, such as Ekedahl-Oort strata, length strata and central leaves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-18T06:08:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke eigenvalues",
      "abelian type compact shimura variety",
      "noncompact shimura varieties",
      "automorphic line bundles",
      "coherent cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}