{
  "id": "2304.04701",
  "version": "v1",
  "published": "2023-04-10T16:41:36.000Z",
  "updated": "2023-04-10T16:41:36.000Z",
  "title": "Explicit computation of Galois representations occurring in families of curves",
  "authors": [
    "Nicolas Mascot"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We extend our method to compute division polynomials of Jacobians of curves over Q to curves over Q(t), in view of computing mod ell Galois representations occurring in the \\'etale cohomology of surfaces over Q. Although the division polynomials which we obtain are unfortunately too complicated to achieve this last goal, we still obtain explicit families of Galois representations over P^1_Q, and we study their degeneration at places of bad reduction of the corresponding curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-10T16:41:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y40",
      "11F80",
      "14D06",
      "14H40",
      "14F20",
      "14Q10"
    ],
    "keywords": [
      "explicit computation",
      "division polynomials",
      "computing mod ell galois representations",
      "mod ell galois representations occurring",
      "bad reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}