{
  "id": "1107.2266",
  "version": "v1",
  "published": "2011-07-12T12:36:06.000Z",
  "updated": "2011-07-12T12:36:06.000Z",
  "title": "A congruence property of the local Langlands correspondence",
  "authors": [
    "Colin J. Bushnell",
    "Guy Henniart"
  ],
  "comment": "14 pages",
  "doi": "10.1093/imrn/rnt063",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\\ell$ a prime number, $\\ell \\neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of $F$ and irreducible cuspidal representations of $\\text{\\rm GL}_n(F)$. We use an explicit description of the correspondence from an earlier paper, and otherwise entirely elementary methods, to show that it respects the relationship of congruence modulo $\\ell$. The $\\ell$-modular correspondence thereby becomes as effective as the complex one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-12T12:36:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "local langlands correspondence",
      "congruence property",
      "non-archimedean local field",
      "congruence modulo",
      "elementary methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.2266B"
    }
  }
}