{
  "id": "1104.0321",
  "version": "v1",
  "published": "2011-04-02T15:37:30.000Z",
  "updated": "2011-04-02T15:37:30.000Z",
  "title": "The local Langlands correspondence for GL_n in families",
  "authors": [
    "Matthew Emerton",
    "David Helm"
  ],
  "comment": "61 papers",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local ring A with finite residue field k of characteristic p different from l. We consider the problem of associating to any such representation an admissible A[GL_n(E)]-module in a manner compatible with the local Langlands correspondence at characteristic zero points of Spec A. In particular we give a set of conditions that uniquely characterise such an A[GL_n(E)]-module if it exists, and show that such an A[GL_n(E)]-module always exists when A is the ring of integers of a finite extension of Q_p. We also use these results to define a \"modified mod p local Langlands correspondence\" that is more compatible with specialization of Galois representations than the mod p local Langlands correspondence of Vigneras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-02T15:37:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S37",
      "11F33",
      "11F70",
      "22E50"
    ],
    "keywords": [
      "local langlands correspondence",
      "complete noetherian local ring",
      "characteristic zero points",
      "reduced complete noetherian local",
      "finite residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0321E"
    }
  }
}