{
  "id": "0911.3132",
  "version": "v1",
  "published": "2009-11-16T20:18:51.000Z",
  "updated": "2009-11-16T20:18:51.000Z",
  "title": "Grothendieck-Serre conjecture for groups of type F_4 with trivial f_3 invariant",
  "authors": [
    "Victor Petrov",
    "Anastasia Stavrova"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "Let R be a semi-local regular ring containing an infinite perfect field, and let K be the field of fractions of R. Let H be a simple algebraic group of type F_4 over R such that H_K is the automorphism group of a 27-dimensional Jordan algebra which is a first Tits construction. If char K is not 2, this means precisely that the f_3 invariant of H_K is trivial. We prove that if an H-torsor is rationally trivial, then it is trivial over R. This result is a particular case of the Grothendieck-Serre conjecture. It continues the recent series of papers by I. Panin, N.Vavilov and the authors, and complements the result of V. Chernousov on the Grothendieck-Serre conjecture for groups of type F_4 with trivial g_3 invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-16T20:18:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grothendieck-serre conjecture",
      "infinite perfect field",
      "simple algebraic group",
      "first tits construction",
      "semi-local regular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.3132P"
    }
  }
}