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Slices of hermitian
$K$–theory and Milnor's conjecture on quadratic forms
Oliver Röndigs and Paul Arne Østvær |
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Geometry & Topology 20 (2016) 1157–1212
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Abstract |
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We advance the understanding of –theory of quadratic forms by computing the slices of the motivic spectra representing hermitian –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 –groups in terms of motivic cohomology. |
Keywords
motivic cohomology, quadratic forms, slices of hermitian
$K$–theory and Witt theory
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Mathematical Subject Classification 2010
Primary: 11E04, 14F42, 55P42
Secondary: 19D50, 19G38, 55T05
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References |
Publication
Received: 29 January 2015
Revised: 2 May 2015
Accepted: 23 June 2015
Published: 28 April 2016
Proposed: Jesper Grodal
Seconded: Paul Goerss, Ronald Stern
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Authors |
| Oliver Röndigs | |
| Institut für Mathematik Universität Osnabrück D-49069 Osnabrück Germany |
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| Paul Arne Østvær | |
| Department of Mathematics University of Oslo PO Box 1053 0316 Oslo Norway |
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