{
  "id": "1002.0492",
  "version": "v1",
  "published": "2010-02-02T14:07:22.000Z",
  "updated": "2010-02-02T14:07:22.000Z",
  "title": "On the modularity level of modular abelian varieties over number fields",
  "authors": [
    "Enrique Gonzalez-Jimenez",
    "Xavier Guitart"
  ],
  "journal": "J. Number Theory 130, no. 7, 1560-1570 (2010)",
  "doi": "10.1016/j.jnt.2010.03.003",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let f be a weight two newform for Gamma_1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety A_f over certain number fields L. The strategy we follow is to compute the restriction of scalars Res_{L/\\Q}(B), and then to apply Milne's formula for the conductor of the restriction of scalars. In this way we obtain an expression for the local exponents of the conductor N_L(B). Under some hypothesis it is possible to give global formulas relating this conductor with N. For instance, if N is squarefree we find that N_L(B) belongs to Z and N_L(B)*f_L^{dim B}=N^{dim B}, where f_L is the conductor of L.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-02T14:07:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular abelian varieties",
      "number fields",
      "modularity level",
      "complex multiplication",
      "apply milnes formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.0492G"
    }
  }
}