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arXiv · 1811.03940

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

Jonas Irgens Kylling·Oliver Röndigs·Paul Arne Østvær
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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.

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Jonas Irgens Kylling, Oliver Röndigs, Paul Arne Østvær. 2018-11-09. Hermitian $K$-theory, Dedekind $\zeta$-functions, and quadratic forms over rings of integers in number fields. https://doi.org/10.4310/cjm.2020.v8.n3.a3

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