Hermitian K-theory of totally real 2-regular number fields, by A. J. Berrick, M. Karoubi, and P. A. Østvær

[Feb 28, 2010: the authors provide an updated and expanded version of the paper, replacing the one submitted Mar 14, 2009.]

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 "Bokstedt 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.

A. J. Berrick <berrick@math.nus.edu.sg>
M. Karoubi <max.karoubi@gmail.com>
P. A. Østvær <paularne@math.uio.no>