Hermitian K-theory, Dedekind zeta-functions, and quadratic forms over rings of integers in number fields

Autor(en): Kylling, Jonas Irgens
Roendigs, Oliver 
Ostvaer, Paul Arne
Stichwörter: algebraic K-theory; CONJECTURE; Hermitian K-theory; higher Witt-theory; HOMOTOPY LIMIT PROBLEM; Mathematics; MOTIVIC COHOMOLOGY; Motivic homotopy theory; quadratic forms over rings of integers; slice filtration; SLICES; special values of Dedekind zeta-functions of number fields
Erscheinungsdatum: 2020
Herausgeber: INT PRESS BOSTON, INC
Journal: CAMBRIDGE JOURNAL OF MATHEMATICS
Volumen: 8
Ausgabe: 3
Startseite: 505
Seitenende: 607
Zusammenfassung: 
We employ the slice spectral sequence, the motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian K-groups of rings of integers in number fields. Moreover, we relate the orders of these groups to special values of Dedekind zeta-functions for totally real abelian number fields. Our methods apply more readily to the examples of algebraic K-theory and higher Witt-theory, and give a complete set of invariants for quadratic forms over rings of integers in number fields.
ISSN: 21680930

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