{
  "id": "2003.07389",
  "version": "v1",
  "published": "2020-03-16T18:12:53.000Z",
  "updated": "2020-03-16T18:12:53.000Z",
  "title": "On $\\mathsf{G}$-isoshtukas over function fields",
  "authors": [
    "Paul Hamacher",
    "Wansu Kim"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "In this paper we classify isogeny classes of global $\\mathsf{G}$-shtukas over a smooth projective curve $C/\\mathbb{F}_q$ (or equivalently $\\sigma$-conjugacy classes in $\\mathsf{G}(\\mathsf{F} \\otimes_{\\mathbb{F}_q} \\overline{\\mathbb{F}_q})$ where $\\mathsf{F}$ is the field of rational functions of $C$) by two invariants $\\bar\\kappa,\\bar\\nu$ extending previous works of Kottwitz. This result can be applied to study points of moduli spaces of $\\mathsf{G}$-shtukas and thus is helpful to calculate their cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-16T18:12:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R32",
      "14K10",
      "20G30"
    ],
    "keywords": [
      "function fields",
      "isoshtukas",
      "moduli spaces",
      "classify isogeny classes",
      "conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}