Please use this identifier to cite or link to this item: https://doi.org/10.1017/is011004009jkt151
Title: Periodicity of hermitian K-groups
Authors: Berrick, A.J. 
Karoubi, M.
Østvær, P.A.
Keywords: Bott periodicity
étale cohomology
higher hermitian K-groups
KSC-theories
Issue Date: Jun-2011
Source: Berrick, A.J., Karoubi, M., Østvær, P.A. (2011-06). Periodicity of hermitian K-groups. Journal of K-Theory 7 (3) : 429-493. ScholarBank@NUS Repository. https://doi.org/10.1017/is011004009jkt151
Abstract: Bott periodicity for the unitary and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients, similar results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodicity for the hermitian K-groups, analogous to orthogonal and symplectic topological K-theory. The proofs use in an essential way higher KSC-theories, extending those of Anderson and Green. They also provide an upper bound for the higher hermitian K-groups in terms of higher algebraic K-groups. We also relate periodicity to étale hermitian K-groups by proving a hermitian version of Thomason's étale descent theorem. The results are illustrated in detail for local fields, rings of integers in number fields, smooth complex algebraic varieties, rings of continuous functions on compact spaces, and group rings. © Copyright ISOPP 2011.
Source Title: Journal of K-Theory
URI: http://scholarbank.nus.edu.sg/handle/10635/103932
ISSN: 18652433
DOI: 10.1017/is011004009jkt151
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