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LOCALIZATION IN HERMITIAN $K$-THEORY OF RINGS

Published online by Cambridge University Press:  23 July 2004

JENS HORNBOSTEL  and
MARCO SCHLICHTING
JENS HORNBOSTEL
Affiliation:
NWF I – Mathematik, Universität Regensburg, 93040 Regensburg, Germanyjens.hornbostel@mathematik.uni-regensburg.de
MARCO SCHLICHTING
Affiliation:
Fb 6 Mathematik, Universität Duisburg-Essen, 45117 Essen, Germanymarco.schlichting@uni-essen.de
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Abstract

Localization and dévissage theorems are proved for the hermitian $K$-theory of rings that are analogous to well-known theorems in algebraic $K$-theory. The proofs rely on, among other things, a study of derived categories, a generalization of a theorem of Pedersen and Weibel to the hermitian setting, and a cofinality result for triangular Witt groups. Applications include a proof of a conjecture of Karoubi and algebraic Bott periodicity.

Keywords

19G38 (primary)18F2519G12 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 77 - 124
Copyright
The London Mathematical Society 2004

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