{
  "id": "math/0607476",
  "version": "v4",
  "published": "2006-07-19T19:47:59.000Z",
  "updated": "2008-03-07T12:03:52.000Z",
  "title": "J-invariant of linear algebraic groups",
  "authors": [
    "Victor Petrov",
    "Nikita Semenov",
    "Kirill Zainoulline"
  ],
  "comment": "The paper containes 39 pages and uses XYPIC package",
  "journal": "Ann. Sci. Ecole Norm. Sup. (4) 41 (2008), no.6, 1023-1053.",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let G be a linear algebraic group over a field F and X be a projective homogeneous G-variety such that G splits over the function field of X. In the present paper we introduce an invariant of G called J-invariant which characterizes the motivic behaviour of X. This generalizes the respective notion invented by A. Vishik in the context of quadratic forms. As a main application we obtain a uniform proof of all known motivic decompositions of generically split projective homogeneous varieties (Severi-Brauer varieties, Pfister quadrics, maximal orthogonal Grassmannians, G2- and F4-varieties) as well as provide new examples (exceptional varieties of types E6, E7 and E8). We also discuss relations with torsion indices, canonical dimensions and cohomological invariants of the group G.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-03-07T12:03:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14M15"
    ],
    "keywords": [
      "linear algebraic group",
      "j-invariant",
      "maximal orthogonal grassmannians",
      "motivic decompositions",
      "function field"
    ],
    "tags": [
      "research tool",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7476P"
    }
  }
}