{
  "id": "0711.3023",
  "version": "v2",
  "published": "2007-11-19T21:47:31.000Z",
  "updated": "2008-08-04T13:56:17.000Z",
  "title": "Stacky Abelianization of an Algebraic Group",
  "authors": [
    "Masoud Kamgarpour"
  ],
  "comment": "22 Pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let G be a connected algebraic group and let [G,G] be its commutator subgroup. We prove a conjecture of Drinfeld about the existence of a connected etale group cover H of [G,G], characterized by the following properties: every central extension of G, by a finite etale group scheme, splits over H, and the commutator map of G lifts to H. We prove, moreover, that the quotient stack of G by the natural action of H is the universal Deligne-Mumford Picard stack to which G maps.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-04T13:56:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic group",
      "stacky abelianization",
      "universal deligne-mumford picard stack",
      "finite etale group scheme",
      "connected etale group cover"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3023K"
    }
  }
}