{
  "id": "0905.1427",
  "version": "v3",
  "published": "2009-05-09T20:09:50.000Z",
  "updated": "2009-12-25T21:55:02.000Z",
  "title": "Grothendieck-Serre conjecture for adjoint groups of types E_6 and E_7 and for certain classical groups",
  "authors": [
    "I. Panin",
    "V. Petrov",
    "A. Stavrova"
  ],
  "comment": "3 pages",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "Assume that R is a semi-local regular ring containing an infinite perfect field, or that R is a semi-local ring of several points on a smooth scheme over an infinite field. Let K be the field of fractions of R. Let H be a strongly inner adjoint simple algebraic group of type E_6 or E_7 over R, or any twisted form of one of the split groups of classical type O^+_{n,R}, n>=4; PGO_{n,R}, n>=4; PSp_{2n,R}, n>=2; PGL_{n,R}, n>=2. We prove that the kernel of the map H^1_{et}(R,H)-> H^1_{et}(K,H) induced by the inclusion of R into K is trivial. This continues the recent series of papers by the authors and N. Vavilov on the Grothendieck--Serre conjecture.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-12-25T21:55:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grothendieck-serre conjecture",
      "adjoint groups",
      "classical groups",
      "inner adjoint simple algebraic group",
      "strongly inner adjoint simple algebraic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1427P"
    }
  }
}