Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00208-010-0503-9
Title: Hermitian K-theory and 2-regularity for totally real number fields
Authors: Berrick, A.J. 
Karoubi, M.
Østvær, P.A.
Issue Date: 2011
Citation: Berrick, A.J., Karoubi, M., Østvær, P.A. (2011). Hermitian K-theory and 2-regularity for totally real number fields. Mathematische Annalen 349 (1) : 117-159. ScholarBank@NUS Repository. https://doi.org/10.1007/s00208-010-0503-9
Abstract: We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. Moreover, the 2-regular case is precisely the class of totally real number fields that have homotopy cartesian "Bökstedt square", relating the K-theory of the 2-integers to that of the fields of real and complex numbers and finite fields. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8 in the orthogonal case. In both the orthogonal and symplectic cases, we prove a 2-primary hermitian homotopy limit conjecture for these rings. © 2010 Springer-Verlag.
Source Title: Mathematische Annalen
URI: http://scholarbank.nus.edu.sg/handle/10635/103368
ISSN: 00255831
DOI: 10.1007/s00208-010-0503-9
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