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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.

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute, Tbilisi State University, University Street 2, Tbilisi, 380043, Georgia

    Hvedri Inassaridze & Tamaz Kandelaki

  2. Tbilisi Centre for Mathematical Sciences, Chavchavadze Ave. 75 3/35, Tbilisi, 0168, Georgia

    Hvedri Inassaridze & Tamaz Kandelaki

  3. Mathematisches Institut and Courant Centre “Higher order structures”, Georg-August Universität Göttingen, Bunsenstraße 3–5, 37073, Göttingen, Germany

    Ralf Meyer

Authors
  1. Hvedri Inassaridze
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  2. Tamaz Kandelaki
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  3. Ralf Meyer
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Corresponding author

Correspondence to Ralf Meyer.

Additional information

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.

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Inassaridze, H., Kandelaki, T. & Meyer, R. Localisation and colocalisation of KK-theory. Abh. Math. Semin. Univ. Hambg. 81, 19–34 (2011). https://doi.org/10.1007/s12188-011-0050-7

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  • DOI: https://doi.org/10.1007/s12188-011-0050-7

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