{
  "id": "math/0204081",
  "version": "v2",
  "published": "2002-04-07T21:04:59.000Z",
  "updated": "2003-10-24T17:34:11.000Z",
  "title": "On a vanishing conjecture appearing in the geometric Langlands correspondence",
  "authors": [
    "D. Gaitsgory"
  ],
  "comment": "Revised version",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth complete curve, and let $Bun_n$ be the moduli stack of rank $n$ vector bundles on $X$. Let $E$ be a local system on $X$. In a recent paper of E.Frenkel, K.Vilonen and the author, it was shown that the vanishing of a certian functor $Av_E^d$ acting from the category $D(Bun_n)$ to itself, implies the geometric Langlands conjecture. In this paper we establish the required vanishing result. Our proof works for sheaves with char=0 coefficients, or with torsion coefficients when the parameter $d$ is less than the characteristic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-10-24T17:34:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric langlands correspondence",
      "vanishing conjecture appearing",
      "smooth complete curve",
      "geometric langlands conjecture",
      "certian functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 610354,
      "adsabs": "2002math......4081G"
    }
  }
}