{
  "id": "0911.4170",
  "version": "v3",
  "published": "2009-11-21T09:55:23.000Z",
  "updated": "2011-03-13T09:34:37.000Z",
  "title": "Isotropy of orthogonal involutions",
  "authors": [
    "Nikita A. Karpenko"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG",
    "math.RA"
  ],
  "abstract": "An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree extension of the base field (provided that the characteristic of the base field is not 2). The proof makes use of a structure theorem for Chow motives with finite coefficients of projective homogeneous varieties, of incompressibility of certain generalized Severi-Brauer varieties, and of Steenrod operations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-13T09:34:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L17",
      "14C25"
    ],
    "keywords": [
      "orthogonal involution",
      "finite odd degree extension",
      "base field",
      "central simple algebra",
      "generalized severi-brauer varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4170K"
    }
  }
}