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.
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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}
}