An exact sequence for Milnor's K-theory with applications to quadratic forms, by Dmitry Orlov, Alexander Vishik, and Vladimir Voevodsky

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. (This is the same paper as before - just a few small mistakes are corrected.)


Dmitry Orlov <orlov@mi.ras.ru>
Alexander Vishik <vishik@mccme.ru>
Vladimir Voevodsky <vladimir@ias.edu>