Localisation and colocalisation of KK-theory at sets of primes
Hvedri Inassaridze, Tamaz Kandelaki, Ralf Meyer
TL;DR
This paper develops a method to localize equivariant Kasparov theory at a set of primes by tensoring with S-integers and compares it with the original theory through exact sequences, enhancing understanding of its algebraic structure.
Contribution
It introduces a new localization technique for KK-theory at sets of primes and analyzes its properties and relationship with the original theory.
Findings
Localization at S preserves key properties of KK-theory.
Exact sequences relate localized and original KK-theory.
Framework facilitates analysis of KK-theory over different prime sets.
Abstract
Given a set of prime numbers S, we localise equivariant bivariant Kasparov theory at S and compare this localisation with Kasparov theory by an exact sequence. More precisely, we define the localisation at S to be KK^G(A,B) tensored with the ring of S-integers Z[S^-1]. We study the properties of the resulting variants of Kasparov theory.
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