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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
Article

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.

Keywords

Exact Sequence Short Exact Sequence Homotopy Type Homotopy Group Homotopy Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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