{
  "id": "1706.03380",
  "version": "v1",
  "published": "2017-06-11T17:19:14.000Z",
  "updated": "2017-06-11T17:19:14.000Z",
  "title": "Frobenius elements in Galois representations with SL_n image",
  "authors": [
    "Matthew Bisatt"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Suppose we have a elliptic curve over a number field whose mod $l$ representation has image isomorphic to $SL_2(\\mathbb{F}_l)$. We present a method to determine Frobenius elements of the associated Galois group which incorporates the linear structure available. We are able to distinguish $SL_n(\\mathbb{F}_l)$-conjugacy from $GL_n(\\mathbb{F}_l)$-conjugacy; this can be thought of as being analogous to a result which distinguishes $A_n$-conjugacy from $S_n$-conjugacy when the Galois group is considered as a permutation group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-11T17:19:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois representations",
      "determine frobenius elements",
      "number field",
      "associated galois group",
      "elliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}