Periodicity of hermitian K-theory and Milnor's K-groups
K-Theory and Homology
2007-05-23 v1 Algebraic Topology
Abstract
We use recent results proved by Berrick and the author (math.KT/0509404) to improve the periodicity theorem in hermitian K-theory. We define also a new filtration of the classical Witt ring W(A), built from non degenerate quadratic forms over any commutative ring A where 2 is invertible. This filtration is linked to the Milnor and Quillen K-groups. Using the solution of Milnor's conjecture by Voevodsky, we show that the non triviality of Milnor's K-groups mod. 2 implies also the non triviality of higher Witt groups (when A is a field).
Keywords
Cite
@article{arxiv.math/0509453,
title = {Periodicity of hermitian K-theory and Milnor's K-groups},
author = {Max Karoubi},
journal= {arXiv preprint arXiv:math/0509453},
year = {2007}
}
Comments
9 pages ; see also http://www.math.jussieu.fr/~karoubi/