{
  "id": "1009.6072",
  "version": "v2",
  "published": "2010-09-30T09:13:38.000Z",
  "updated": "2010-10-14T10:13:31.000Z",
  "title": "An effective isomorphy criterion for mod $\\ell$ Galois representations",
  "authors": [
    "Yuuki Takai"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we consider mod $\\ell$ Galois representations of $\\mathbb{Q}$. In particular, we obtain an effective criterion to distinguish two semisimple 2-dimensional, odd mod $\\ell$ Galois representations up to isomorphism. Serre's conjecture (Khare-Wintenberger's theorem), Sturm's theorem, and its modification by Kohnen are used in our proof.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-14T10:13:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F33"
    ],
    "keywords": [
      "galois representations",
      "effective isomorphy criterion",
      "odd mod",
      "serres conjecture",
      "khare-wintenbergers theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.6072T"
    }
  }
}