{
  "id": "1911.02141",
  "version": "v1",
  "published": "2019-11-05T23:39:48.000Z",
  "updated": "2019-11-05T23:39:48.000Z",
  "title": "Automorphic Galois repesentations and the inverse Galois problem for certain groups of type $D_{2m}$",
  "authors": [
    "Adrian Zenteno"
  ],
  "comment": "Preliminary version, comments are welcome",
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "Let $\\ell$ be an odd prime and $m$ be a positive integer greater than two. In this paper, we prove that at least one of the following groups: $\\mbox{P}\\Omega^\\pm_{4m}(\\mathbb{F}_{\\ell^s})$, $\\mbox{PSO}^\\pm_{4m}(\\mathbb{F}_{\\ell^s})$, $\\mbox{PO}_{4m}^\\pm(\\mathbb{F}_{\\ell^s})$ or $\\mbox{PGO}^\\pm_{4m}(\\mathbb{F}_{\\ell^s})$ is a Galois group of $\\mathbb{Q}$ for infinitely many integers $s > 0$. This is achieved by making use of a slight modification of a group theory result of Khare, Larsen and Savin, and previous results of the author on the images of the Galois representations attached to cuspidal automorphic representations of $\\mbox{GL}_{4m}(\\mathbb{A}_\\mathbb{Q})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-05T23:39:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "12F12",
      "20G40"
    ],
    "keywords": [
      "inverse galois problem",
      "automorphic galois repesentations",
      "cuspidal automorphic representations",
      "group theory result",
      "positive integer greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}