We advance the understanding of K–theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K–groups andWitt groups. By an explicit computation of the slice spectral sequence for higher Witt theory, we prove Milnor’s conjecture relating Galois cohomology to quadratic forms via the filtration of the Witt ring by its fundamental ideal. In a related computation we express hermitian K–groups in terms of motivic cohomology.

Slices of hermitian K–theory and milnor’s conjecture on quadratic forms / O. Rondigs, P.A. Oestvaer. - In: GEOMETRY & TOPOLOGY. - ISSN 1465-3060. - 20:2(2016), pp. 1157-1212. [10.2140/gt.2016.20.1157]

Slices of hermitian K–theory and milnor’s conjecture on quadratic forms

P.A. Oestvaer
2016

Abstract

We advance the understanding of K–theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K–groups andWitt groups. By an explicit computation of the slice spectral sequence for higher Witt theory, we prove Milnor’s conjecture relating Galois cohomology to quadratic forms via the filtration of the Witt ring by its fundamental ideal. In a related computation we express hermitian K–groups in terms of motivic cohomology.
K-theory and Witt theory; Motivic cohomology; Quadratic forms; Slices of hermitian
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/860149
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