Article

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 81, Issue 1, pp 19-34

Localisation and colocalisation of KK-theory

  • Hvedri InassaridzeAffiliated withA. Razmadze Mathematical Institute, Tbilisi State UniversityTbilisi Centre for Mathematical Sciences
  • , Tamaz KandelakiAffiliated withA. Razmadze Mathematical Institute, Tbilisi State UniversityTbilisi Centre for Mathematical Sciences
  • , Ralf MeyerAffiliated withMathematisches Institut and Courant Centre “Higher order structures”, Georg-August Universität Göttingen Email author 

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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.

Keywords

Localisation Triangulated category KK-theory

Mathematics Subject Classification (2000)

19K99 19K35 19D55