{
  "id": "1706.04174",
  "version": "v1",
  "published": "2017-06-13T17:39:19.000Z",
  "updated": "2017-06-13T17:39:19.000Z",
  "title": "On the images of the Galois representations attached to certain RAESDC automorphic representations of $\\mbox{GL}_n(\\mathbb{A}_{\\mathbb{Q}})$",
  "authors": [
    "Adrian Zenteno"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we prove the existence of infinitely many compatible systems $\\{ \\rho_\\ell \\}_\\ell$ of $n$-dimensional Galois representations associated to regular algebraic, essentially self-dual, cuspidal automorphic representations of $\\mbox{GL}_n(\\mathbb{A}_{\\mathbb{Q}})$ ($n$ even) such that the image of $\\overline{\\rho}_{\\ell}^{proj}$ (the projectivization of the reduction of $\\rho_\\ell$) is an almost simple group for almost all primes $\\ell$. Moreover, applying this result to some low-dimensional cases, we prove that the symplectic groups: $\\mbox{PSp}_n(\\mathbb{F}_{\\ell^s})$ and $\\mbox{PGSp}_n(\\mathbb{F}_{\\ell^s})$, for $6\\leq n \\leq 12$, and the orthogonal groups: $\\mbox{P}\\Omega^+_n(\\mathbb{F}_{\\ell^s})$, $\\mbox{PSO}^+_n(\\mathbb{F}_{\\ell^s})$, $\\mbox{PO}^+_n(\\mathbb{F}_{\\ell^s})$ and $\\mbox{PGO}^+_n(\\mathbb{F}_{\\ell^s})$, occurs as Galois groups over $\\mathbb{Q}$ for infinitely many primes $\\ell$ and infinitely many positive integers $s$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T17:39:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "12F12"
    ],
    "keywords": [
      "raesdc automorphic representations",
      "dimensional galois representations",
      "cuspidal automorphic representations",
      "galois groups",
      "regular algebraic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}