{
  "id": "math/0402184",
  "version": "v4",
  "published": "2004-02-11T22:08:05.000Z",
  "updated": "2006-04-01T23:37:33.000Z",
  "title": "On de Jong's conjecture",
  "authors": [
    "Dennis Gaitsgory"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth projective curve over a finite field $F_q$. Let $\\rho$ be a continuous representation $\\pi(X)\\to GL_n(F)$, where $F=F_l((t))$ with $F_l$ being another finite field of order prime to $q$. Assume that $\\rho|_{\\pi(\\bar{X})}$ is irreducible. De Jong's conjecture says that in this case $\\rho(\\pi(\\bar{X}))$ is finite. As was shown in the original paper of de Jong, this conjecture follows from an existence of an $F$-valued automorphic form corresponding to $\\rho$ is the sense of Langlands. The latter follows, in turn, from a version of the Geometric Langlands conjecture. In this paper we sketch a proof of the required version of the geometric conjecture, assuming that $char(F)\\neq 2$, thereby proving de Jong's conjecture in this case.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-04-01T23:37:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "geometric langlands conjecture",
      "jongs conjecture says",
      "smooth projective curve",
      "order prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2184G"
    }
  }
}