{
  "id": "1712.05528",
  "version": "v1",
  "published": "2017-12-15T04:28:58.000Z",
  "updated": "2017-12-15T04:28:58.000Z",
  "title": "Lübeck's classification of Chevaley groups representations and the inverse Galois problem for some orthogonal groups",
  "authors": [
    "Adrian Zenteno"
  ],
  "comment": "9 pages, preliminary version, comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we prove that for each integer of the form $n=4\\varpi$ (where $\\varpi$ is a prime between $17$ and $73$) at least one of the following groups: $P\\Omega^+_n(\\mathbb{F}_{\\ell^s})$, $PSO^+_n(\\mathbb{F}_{\\ell^s})$, $PO_n^+(\\mathbb{F}_{\\ell^s})$ or $PGO^+_n(\\mathbb{F}_{\\ell^s})$ is a Galois groups of $\\mathbb{Q}$ for almost all primes $\\ell$ and infinitely many integers $s > 0$. This is achieved by making use of the classification of small degree representations of finite Chevalley groups in defining characteristic of F. L\\\"ubeck and a previous result of the author on the image of the Galois representations attached to RAESDC automorphic representations of $GL_n(\\mathbb{A}_\\mathbb{Q})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-15T04:28:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "12F12",
      "20C33"
    ],
    "keywords": [
      "inverse galois problem",
      "chevaley groups representations",
      "lübecks classification",
      "orthogonal groups",
      "raesdc automorphic representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}