{
  "id": "1411.1703",
  "version": "v1",
  "published": "2014-11-06T19:05:07.000Z",
  "updated": "2014-11-06T19:05:07.000Z",
  "title": "Explicit surjectivity for Galois representations attached to abelian surfaces",
  "authors": [
    "Davide Lombardo"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be an absolutely simple abelian surface without (potential) complex multiplication, defined over the number field $K$. We explicitly give a bound $\\ell_0(A,K)$ such that, for every prime $\\ell>\\ell_0(A,K)$, the image of $\\operatorname{Gal}\\left(\\overline{K}/K\\right)$ in $\\operatorname{Aut}(T_\\ell(A))$ is as large as it is allowed to be by endomorphisms and polarizations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-06T19:05:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14K15",
      "11F80"
    ],
    "keywords": [
      "galois representations",
      "explicit surjectivity",
      "absolutely simple abelian surface",
      "complex multiplication",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1703L"
    }
  }
}