{
  "id": "2205.03848",
  "version": "v1",
  "published": "2022-05-08T12:22:37.000Z",
  "updated": "2022-05-08T12:22:37.000Z",
  "title": "Local Langlands correspondences",
  "authors": [
    "Michael Harris"
  ],
  "comment": "For the proceedings of the conference \"Theta Series: Representation Theory, Geometry, and Arithmetic\" in honor of Steve Kudla's 70th birthday",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "The first part of this article is a review of the properties expected of any local Langlands correspondence that aims to be considered \"canonical,\" and of known results that establish some or all of these properties for specific groups. In the absence of compatibility with a global correspondence it is not known in general that this list of desirable properties suffices to characterize the correspondence. The remainder of the article outlines elements of a strategy to prove that the $L$-packets attached to irreducible local parameters are finite and non-empty, in particular, for the specific parametrization constructed by Genestier and Lafforgue when $F$ is of positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-08T12:22:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S37",
      "22E50"
    ],
    "keywords": [
      "local langlands correspondence",
      "article outlines elements",
      "specific groups",
      "first part",
      "desirable properties suffices"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}