{
  "id": "1711.11159",
  "version": "v1",
  "published": "2017-11-29T23:50:58.000Z",
  "updated": "2017-11-29T23:50:58.000Z",
  "title": "On the local converse theorem and the descent theorem in families",
  "authors": [
    "Baiying Liu",
    "Gilbert Moss"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an analogue of Jacquet's conjecture on the local converse theorem for \\ell-adic families of co-Whittaker representations of GL_n(F), where F is a finite extension of Q_p and \\ell does not equal p. We also prove an analogue of Jacquet's conjecture for a descent theorem, which asks for the smallest collection of gamma factors determining the subring of definition of an \\ell-adic family. These two theorems are closely related to the local Langlands correspondence in \\ell-adic families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-29T23:50:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "22E50",
      "11F85"
    ],
    "keywords": [
      "local converse theorem",
      "descent theorem",
      "jacquets conjecture",
      "local langlands correspondence",
      "co-whittaker representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}