{
  "id": "1708.01213",
  "version": "v1",
  "published": "2017-08-03T17:01:08.000Z",
  "updated": "2017-08-03T17:01:08.000Z",
  "title": "Local Langlands correspondence in rigid families",
  "authors": [
    "Christian Johansson",
    "James Newton",
    "Claus Sorensen"
  ],
  "comment": "28 pages, comments are welcome!",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We show that local-global compatibility (at split primes) away from $p$ holds at all points of the $p$-adic eigenvariety of a definite $n$-variable unitary group. The novelty is we allow non-classical points, possibly non-\\'{e}tale over weight space. More precisely we interpolate the local Langlands correspondence for GL(n) across the eigenvariety by considering the fibers of its defining coherent sheaf. We employ techniques of Scholze from his new approach to the local Langlands conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T17:01:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F70",
      "11F80"
    ],
    "keywords": [
      "local langlands correspondence",
      "rigid families",
      "local langlands conjecture",
      "variable unitary group",
      "local-global compatibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}