Periodicity of hermitian K-theory and Milnor's K-groups

Details Periodicity of hermitian K-theory and Milnor's K-groups Periodicity of hermitian K-theory and Milnor's K-groups

2005-09-20

arxiv.org/abs/math/0509453v1

Contemporary Mathematics, volume 344 (2004) 197-206

Mathematics

K-Theory and Homology

9 pages ; see also http://www.math.jussieu.fr/~karoubi/

Scientific paper

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).

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