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Localizing subcategories in the Bootstrap category of separable C*-algebras
Published online by Cambridge University Press: 15 September 2010
Abstract
Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category Boot ⊂ KK of separable complex C*-algebras. Namely, they are in a bijective correspondence with subsets of the Zariski spectrum Specℤ of the integers – precisely as for the localizing subcategories of the derived category D(ℤ) of complexes of abelian groups. We provide corollaries of this fact and put it in context with the similar classifications available in the literature.
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