Localisation and colocalisation of KK-theory



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.


Localisation Triangulated category KK-theory 

Mathematics Subject Classification (2000)

19K99 19K35 19D55 


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Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2011

Authors and Affiliations

  • Hvedri Inassaridze
    • 1
    • 2
  • Tamaz Kandelaki
    • 1
    • 2
  • Ralf Meyer
    • 3
  1. 1.A. Razmadze Mathematical InstituteTbilisi State UniversityTbilisiGeorgia
  2. 2.Tbilisi Centre for Mathematical SciencesTbilisiGeorgia
  3. 3.Mathematisches Institut and Courant Centre “Higher order structures”Georg-August Universität GöttingenGöttingenGermany

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