Mathematische Annalen

, Volume 349, Issue 1, pp 117–159 | Cite as

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

  • A. Jon Berrick
  • Max Karoubi
  • Paul Arne Østvær


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.


Exact Sequence Short Exact Sequence Homotopy Type Homotopy Group Homotopy Theory 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • A. Jon Berrick
    • 1
  • Max Karoubi
    • 2
  • Paul Arne Østvær
    • 3
  1. 1.Department of MathematicsNational University of SingaporeSingaporeSingapore
  2. 2.UFR de MathématiquesUniversité Paris 7ParisFrance
  3. 3.Department of MathematicsUniversity of OsloOsloNorway

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