English

An exact sequence for Milnor's K-theory with applications to quadratic forms

Algebraic Geometry 2018-08-17 v1 K-Theory and Homology

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.

Keywords

Cite

@article{arxiv.math/0101023,
  title  = {An exact sequence for Milnor's K-theory with applications to quadratic forms},
  author = {Dmitry Orlov and Alexander Vishik and Vladimir Voevodsky},
  journal= {arXiv preprint arXiv:math/0101023},
  year   = {2018}
}
R2 v1 2026-07-22T16:36:39.540Z