Hermitian K-theory and 2-regularity for totally real number fields

Details Hermitian K-theory and 2-regularity for totally real number fields Hermitian K-theory and 2-regularity for totally real number fields

2009-03-14

arxiv.org/abs/0903.2545v2

Mathematics

K-Theory and Homology

To appear in Mathematische Annalen

Scientific paper

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. 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 both the orthogonal and symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum conjecture.

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