{
  "id": "1109.2802",
  "version": "v4",
  "published": "2011-09-13T14:41:03.000Z",
  "updated": "2012-09-28T07:07:38.000Z",
  "title": "Prime-to-p étale covers of algebraic groups",
  "authors": [
    "Michel Brion",
    "Tamás Szamuely"
  ],
  "comment": "14 pages, final version, to appear at Bulletin of the London Mathematical Society",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let G be a connected algebraic group over an algebraically closed field of characteristic p (possibly 0), and X a variety on which G acts transitively with connected stabilizers. We show that any \\'etale Galois cover of X of degree prime to p is also homogeneous, and that the maximal prime-to-p quotient of the \\'etale fundamental group of X is commutative. We moreover obtain an explicit bound for the number of topological generators of the said quotient. When G is commutative, we also obtain a description of the prime-to-p torsion in the Brauer group of G.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-09-28T07:07:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E20",
      "14F35",
      "14L10",
      "14M17"
    ],
    "keywords": [
      "etale fundamental group",
      "maximal prime-to-p quotient",
      "etale galois cover",
      "connected algebraic group",
      "brauer group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2802B"
    }
  }
}