{
  "id": "0905.1538",
  "version": "v1",
  "published": "2009-05-11T04:27:22.000Z",
  "updated": "2009-05-11T04:27:22.000Z",
  "title": "Approximating classifying spaces by smooth projective varieties",
  "authors": [
    "Torsten Ekedahl"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "We prove that for every reductive algebraic group $H$ with centre of positive dimension and every integer $K$ there is a smooth and projective variety $X$ and an algebraic $H$-torsor $P \\to X$ such that the classifying map $X \\to \\Bclass H$ induces an isomorphism in cohomology in degrees $\\le K$. This is then applied to show that if $G$ is a connected non-special group there is a $G$-torsor $P \\to X$ for which we do not have $[P]=[G][X]$ in the (completion of the) Grothendieck ring of varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-11T04:27:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R40",
      "14L24",
      "14F25"
    ],
    "keywords": [
      "projective variety",
      "smooth projective varieties",
      "approximating classifying spaces",
      "reductive algebraic group",
      "connected non-special group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1538E"
    }
  }
}