{
  "id": "1007.4004",
  "version": "v7",
  "published": "2010-07-22T20:26:59.000Z",
  "updated": "2018-03-01T16:37:39.000Z",
  "title": "On a conjecture of Deligne",
  "authors": [
    "Vladimir Drinfeld"
  ],
  "comment": "Minor changes in Appendix A",
  "categories": [
    "math.NT",
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let X be a smooth variety over $F_p$. Let E be a number field. For each nonarchimedean place $\\lambda$ of E prime to p consider the set of isomorphism classes of irreducible lisse $\\bar{E}_{\\lambda}$-sheaves on X with determinant of finite order such that for every closed point x in X the characteristic polynomial of the Frobenius $F_x$ has coefficents in E. We prove that this set does not depend on $\\lambda$. The idea is to use a method developed by G.Wiesend to reduce the problem to the case where X is a curve. This case was treated by L. Lafforgue.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2012-03-11T17:46:09.000Z",
      "comment": "The argument in Section 4 has been replaced by a simpler one (due to M. Kerz)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v7",
      "updated": "2018-03-01T16:37:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G15",
      "11G35"
    ],
    "keywords": [
      "conjecture",
      "smooth variety",
      "number field",
      "nonarchimedean place",
      "isomorphism classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4004D"
    }
  }
}