Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms
By O. Rondigs, P. Ostvaer. 2013
56 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/32e9ba3cf62437d65330268a05c630c8c0b5d022
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In Geometry and Topology
- Markus Spitzweck
- O. Rondigs
- P. Ostvaer
- M. Levine
- Denis-Charles Cisinski
- Frédéric Déglise
- John E. Harper
- C. Berger
In Mathematical Physics
- Markus Spitzweck
- O. Rondigs
- P. Ostvaer
- M. Levine
- Denis-Charles Cisinski
- Frédéric Déglise
- John E. Harper
- C. Berger
Citations in the corpus
- The first stable homotopy groups of motivic spheres (2016, methodology): “ and compatible with pullbacks. Proof. The proof of cellularity given in [64] carries over to the setting of compatible pairs. 11 Next we extend the computation of the slices of hermitian K-theory in [63]. This will be used to analyze the map between slices induced by the unit map 1 Λ→KQ . Theorem 2”