Localizing subcategories in the Bootstrap category of separable C*-algebras

Abstract

Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category of separable complex C*-algebras. Namely, they are in bijective correspondence with subsets of the Zariski spectrum of the integers -- precisely as for the localizing subcategories of the derived category of complexes of abelian groups. We provide corollaries of this fact and put it in context with similar classifications available in the literature.