{
  "id": "2008.00556",
  "version": "v1",
  "published": "2020-08-02T20:05:37.000Z",
  "updated": "2020-08-02T20:05:37.000Z",
  "title": "On the images of certain $G_2$-valued automorphic Galois representations",
  "authors": [
    "Adrian Zenteno"
  ],
  "comment": "Preliminary version, comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study the images of certain families $\\{\\rho_{\\pi,\\lambda} \\}_\\lambda$ of $G_2$-valued Galois representations associated to algebraic regular, self-dual, cuspidal automorphic representations $\\pi$ of $\\mbox{GL}_7(\\mathbb{A}_\\mathbb{Q})$. In particular, we prove that under certain conditions in the weights of $\\pi$ the images of the residual representations $\\overline{\\rho}_{\\pi,\\lambda}$ are as large as possible for infinitely many primes $\\lambda$ and provide some examples where such conditions are satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-02T20:05:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "20G41"
    ],
    "keywords": [
      "valued automorphic galois representations",
      "cuspidal automorphic representations",
      "valued galois representations",
      "algebraic regular",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}