Date: 17 Mar 2011

Localisation and colocalisation of KK-theory

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Abstract

The localisation of an R-linear triangulated category  \(\mathcal{T}\) at S −1 R for a multiplicatively closed subset S is again triangulated, and related to the original category by a long exact sequence involving a version of  \(\mathcal{T}\) with coefficients in S −1 R/R. We examine these theories and, under some assumptions, write the latter as an inductive limit of  \(\mathcal{T}\) with torsion coefficients. Our main application is the case where  \(\mathcal{T}\) is equivariant bivariant K-theory and R the ring of integers.

Communicated by B. Richter.
This research was supported by the Volkswagen Foundation (Georgian–German non-commutative partnership). The third author was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.