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Localization in Hermitian K ‐Theory of Rings
Author(s) -
Hornbostel Jens,
Schlichting Marco
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005393
Subject(s) - hermitian matrix , mathematical proof , generalization , mathematics , algebraic number , conjecture , pure mathematics , algebra over a field , algebraic theory , algebraic structure , cofinality , discrete mathematics , mathematical analysis , geometry , uncountable set , countable set
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.