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 | Enthalten in: | CAMBRIDGE JOURNAL OF MATHEMATICS | Band: | 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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