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19g38 (primary)

Journal of the London Mathematical Society (1)

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LOCALIZATION IN HERMITIAN $K$-THEORY OF RINGS
JENS HORNBOSTEL, MARCO SCHLICHTING
Journal:

Journal of the London Mathematical Society / Volume 70 / Issue 1 / August 2004

Published online by Cambridge University Press:

23 July 2004, pp. 77-124

Print publication:

August 2004
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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.