An exact sequence for Milnor's Ktheory with applications to quadratic forms
Abstract
We construct a fourterm exact sequence which provides information on the kernel and cokernel of the multiplication by a pure symbol in Milnor's Ktheory 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 KhanRostSujatha conjecture and the Jfiltration conjecture. The first version of this paper was written in the spring of 1996.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2001
 arXiv:
 arXiv:math/0101023
 Bibcode:
 2001math......1023O
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology;
 12Gxx;
 11Exx
 EPrint:
 Ann. of Math. (2) 165 (2007), no. 1, 113