Periodicity of Hermitian K-theory and Milnor's K-groups, by Max Karoubi

In this paper, we use the recent results proved by J. Berrick and the author (../0649/) to improve the periodicity theorem in Hermitian K-theory and define a new filtration of the classical Witt ring W(A) of non degenerate quadratic forms, for any commutative ring A with 2 invertible. This filtration is linked to the Milnor and Quillen K-groups. Using the solution of the Milnor conjecture by Voevodsky, we show that the non triviality of the Milnor K-groups mod. 2 implies also the non triviality of the higher Witt groups (when A is a field).

Max Karoubi <>