{
  "id": "1803.03791",
  "version": "v1",
  "published": "2018-03-10T10:39:50.000Z",
  "updated": "2018-03-10T10:39:50.000Z",
  "title": "Shtukas for reductive groups and Langlands correspondence for function fields",
  "authors": [
    "Vincent Lafforgue"
  ],
  "comment": "ICM report",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We discuss recent developments in the Langlands program for function fields, and in the geometric Langlands program. In particular we explain a canonical decomposition of the space of cuspidal automorphic forms for any reductive group G over a function field, indexed by global Langlands parameters. The proof uses the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-10T10:39:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35",
      "14H60",
      "11F70"
    ],
    "keywords": [
      "function field",
      "reductive group",
      "langlands correspondence",
      "cuspidal automorphic forms",
      "geometric langlands program"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}