{
  "id": "1007.0358",
  "version": "v2",
  "published": "2010-07-02T13:05:44.000Z",
  "updated": "2010-10-23T07:42:30.000Z",
  "title": "$m$-bigness in compatible systems",
  "authors": [
    "Paul-James White"
  ],
  "journal": "C. R. Acad. Sci. Paris, Ser. I 348 (2010) 1049-1054",
  "doi": "10.1016/j.crma.2010.09.001",
  "categories": [
    "math.NT"
  ],
  "abstract": "Taylor-Wiles type lifting theorems allow one to deduce that for $\\rho$ a \"sufficiently nice\" $l$-adic representation of the absolute Galois group of a number field whose semi-simplified reduction modulo $l$, denoted $\\overline{\\rho}$, comes from an automorphic representation then so does $\\rho$. The recent lifting theorems of Barnet-Lamb-Gee-Geraghty-Taylor impose a technical condition, called \\emph{$m$-big}, upon the residual representation $\\overline{\\rho}$. Snowden-Wiles proved that for a sufficiently irreducible compatible system of Galois representations, the residual images are \\emph{big} at a set of places of Dirichlet density $1$. We demonstrate the analogous result in the \\emph{$m$-big} setting using a mild generalization of their argument.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-23T07:42:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80"
    ],
    "keywords": [
      "compatible system",
      "taylor-wiles type lifting theorems",
      "absolute galois group",
      "mild generalization",
      "number field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0358W"
    }
  }
}