{
  "id": "2009.06708",
  "version": "v1",
  "published": "2020-09-14T19:46:03.000Z",
  "updated": "2020-09-14T19:46:03.000Z",
  "title": "Moduli of Langlands Parameters",
  "authors": [
    "Jean-François Dat",
    "David Helm",
    "Robert Kurinczuk",
    "Gilbert Moss"
  ],
  "comment": "79 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $F$ be a nonarchimedean local field of residue characteristic $p$, let $\\hat{G}$ be a split connected reductive group over $\\mathbb{Z}[1/p]$ with an action of $W_F$, and let $^LG$ denote the semidirect product $\\hat{G}\\rtimes W_F$. We construct a moduli space of Langlands parameters $W_F \\to {^LG}$, and show that it is locally of finite type and flat over $\\mathbb{Z}[1/p]$, and that it is a reduced local complete intersection. We give parameterizations of the connected components of this space over algebraically closed fields of characteristic zero and characteristic $\\ell\\neq p$, as well as of the components over $\\overline{\\mathbb{Z}}_{\\ell}$ and (conjecturally) over $\\overline{\\mathbb{Z}}[1/p]$. Finally we study the functions on this space that are invariant under conjugation by $\\hat{G}$ (or, equivalently, the GIT quotient by $\\hat{G}$) and give a complete description of this ring of functions after inverting an explicit finite set of primes depending only on $^LG$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-14T19:46:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F70",
      "22E50"
    ],
    "keywords": [
      "langlands parameters",
      "nonarchimedean local field",
      "reduced local complete intersection",
      "explicit finite set",
      "split connected reductive group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 79,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}