{
  "id": "math/0206147",
  "version": "v4",
  "published": "2002-06-14T19:35:41.000Z",
  "updated": "2004-07-31T16:58:57.000Z",
  "title": "Independence of ell of Monodromy Groups",
  "authors": [
    "CheeWhye Chin"
  ],
  "comment": "25 pages, AMS-LaTeX; journal version",
  "journal": "J. Amer. Math. Soc. 17 (2004), no.3, 723--747",
  "doi": "10.1090/S0894-0347-04-00456-4",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let X be a smooth curve over a finite field of characteristic p, let E be a number field, and consider an E-compatible system of lisse sheaves on the curve X. For each place lambda of E not lying over p, the lambda-component of the system is a lisse E_lambda-sheaf on X, whose associated arithmetic monodromy group is an algebraic group over the local field E_lambda. We use Serre's theory of Frobenius tori and Lafforgue's proof of Deligne's conjecture to show that when the E-compatible system is semisimple and pure of some integer weight, the isomorphism type of the identity component of these monodromy groups is ``independent of lambda''. More precisely: after replacing E by a finite extension, there exists a connected split reductive algebraic group G_0 over the number field E such that for every place lambda of E not lying over p, the identity component of the arithmetic monodromy group of the lambda-component of the system is isomorphic to the group G_0 with coefficients extended to the local field E_lambda.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2004-07-31T16:58:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G10",
      "11G40",
      "14F20"
    ],
    "keywords": [
      "independence",
      "identity component",
      "place lambda",
      "local field",
      "number field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......6147C"
    }
  }
}