{
  "id": "math/0101023",
  "version": "v1",
  "published": "2001-01-03T17:30:18.000Z",
  "updated": "2001-01-03T17:30:18.000Z",
  "title": "An exact sequence for Milnor's K-theory with applications to quadratic forms",
  "authors": [
    "Dmitry Orlov",
    "Alexander Vishik",
    "Vladimir Voevodsky"
  ],
  "journal": "Ann. of Math. (2) 165 (2007), no. 1, 1--13",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We construct a four-term exact sequence which provides information on the kernel and cokernel of the multiplication by a pure symbol in Milnor's K-theory mod 2 of fields of characteristic zero. As an application we establish, for fields of characteristics zero, the validity of three conjectures in the theory of quadratic forms - the Milnor conjecture on the structure of the Witt ring, the Khan-Rost-Sujatha conjecture and the J-filtration conjecture. The first version of this paper was written in the spring of 1996.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-03T17:30:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12Gxx",
      "11Exx"
    ],
    "keywords": [
      "quadratic forms",
      "application",
      "four-term exact sequence",
      "milnors k-theory mod",
      "first version"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......1023O"
    }
  }
}