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Localisation and colocalisation of KK-theory

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

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References (30)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Mathematisches Seminar der Universität Hamburg and Springer
Subject
Mathematics; Algebra; Geometry ; Topology; Number Theory; Combinatorics; Differential Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-011-0050-7
Publisher site
See Article on Publisher Site

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.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Mar 17, 2011

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