{
  "id": "1407.5802",
  "version": "v2",
  "published": "2014-07-22T09:48:42.000Z",
  "updated": "2014-12-10T16:11:27.000Z",
  "title": "Galois representations and Galois groups over Q",
  "authors": [
    "Sara Arias-de-Reyna",
    "Cécile Armana",
    "Valentijn Karemaker",
    "Marusia Rebolledo",
    "Lara Thomas",
    "Núria Vila"
  ],
  "comment": "Minor changes. 13 pages. This paper contains results of the collaboration started at the conference Women in numbers - Europe, (October 2013), by the working group \"Galois representations and Galois groups over Q\"",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that there exists a prime p such that J(C) has semistable reduction with toric dimension 1 at p. We provide an algorithm to compute a list of primes l (if they exist) such that the Galois representation attached to the l-torsion of J(C) is surjective onto the group GSp(2n, l). In particular we realize GSp(6, l) as a Galois group over Q for all primes l in [11, 500000].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-22T09:48:42.000Z",
      "comment": "13 pages. This paper is the result of the collaboration started at the conference Women in numbers - Europe, (October 2013), by the working group \"Galois representations and Galois groups over Q\"",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-10T16:11:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F12",
      "11F80",
      "11G30",
      "11R32"
    ],
    "keywords": [
      "galois group",
      "galois representation",
      "hyperelliptic curves",
      "hyperelliptic genus",
      "toric dimension"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5802A"
    }
  }
}