{
  "id": "math/0206001",
  "version": "v2",
  "published": "2002-06-02T18:28:22.000Z",
  "updated": "2002-06-25T17:35:12.000Z",
  "title": "Independence of l in Lafforgue's theorem",
  "authors": [
    "CheeWhye Chin"
  ],
  "comment": "19 pages, AMSTeX; revised version 2 to appear in Advances in Mathematics",
  "journal": "Adv. Math. 180 (2003), no. 1, 64--86",
  "doi": "10.1016/S0001-8708(02)00082-8",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let X be a smooth curve over a finite field of characteristic p, let l be a prime number different from p, and let L be an irreducible lisse l-adic sheaf on X whose determinant is of finite order. By a theorem of Lafforgue, for each prime number l' different from p, there exists an irreducible lisse l'-adic sheaf L' on X which is compatible with L, in the sense that at every closed point x of X, the characteristic polynomials of Frobenius at x for L and L' are equal. We prove an \"independence of l\" assertion on the fields of definition of these irreducible l'-adic sheaves L' : namely, that there exists a number field F such that for any prime number l' different from p, the l'-adic sheaf L' above is defined over the completion of F at one of its l'-adic places.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-06-25T17:35:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G10",
      "14F20",
      "14G13",
      "14G15"
    ],
    "keywords": [
      "lafforgues theorem",
      "prime number",
      "independence",
      "irreducible lisse l-adic sheaf",
      "smooth curve"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......6001C"
    }
  }
}