an:06578603
Zbl 1416.19001
R??ndigs, Oliver; ??stv??r, Paul
Slices of Hermitian \(K\)-theory and Milnor's conjecture on quadratic forms
EN
Geom. Topol. 20, No. 2, 1157-1212 (2016).
00355309
2016
j
19G38 11E70 11E04 14F42 55P42 55T05
motivic cohomology; quadratic forms; slices of Hermitian \(K\)-theory and Witt theory
Summary: We advance the understanding of \(K\)-theory of quadratic forms by computing the slices of the motivic spectra representing hermitian \(K\)-groups and Witt 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.