{
  "id": "math/0404025",
  "version": "v1",
  "published": "2004-04-02T11:01:37.000Z",
  "updated": "2004-04-02T11:01:37.000Z",
  "title": "Existence of non-elliptic mod l Galois representations for every l >5",
  "authors": [
    "Luis Dieulefait"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For $\\ell = 3$ and 5 it is known that every odd, irreducible, 2-dimensional representation of $\\Gal(\\bar{\\Q}/\\Q)$ with values in $\\F_\\ell$ and determinant equal to the cyclotomic character must \"come from\" the $\\ell$-torsion points of an elliptic curve defined over $\\Q$. We prove, by giving concrete counter-examples, that this result is false for every prime $\\ell >5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-02T11:01:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois representations",
      "non-elliptic mod",
      "cyclotomic character",
      "torsion points",
      "giving concrete counter-examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4025D"
    }
  }
}