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.

Hermitian K-theory, Dedekind zeta-functions, and quadratic forms over rings of integers in number fields [Hermitian $K$-theory, Dedekind $zeta$-functions, and quadratic forms over rings of integers in number fields] / J.I. Kylling, R. Oliver, P.A. Oestvaer. - In: CAMBRIDGE JOURNAL OF MATHEMATICS. - ISSN 2168-0930. - 8:3(2020), pp. 505-607. [10.4310/CJM.2020.v8.n3.a3]

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

P.A. Oestvaer
Ultimo
2020

Abstract

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.
Motivic homotopy theory; slice filtration; motivic cohomology; algebraic K-theory; Hermitian K-theory; higher Witt-theory; quadratic forms over rings of integers; special values of Dedekind zeta-functions of number fields;
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/860133
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