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.

9 pages, simplified proof. Final version, to appear on J. of K-theory

References in corpus (4)

• Stratifying triangulated categories
• Homological algebra in bivariant K-theory and other triangulated categories
• Tensor triangular geometry and KK-theory
• The spectrum of prime ideals in tensor triangulated categories

Cited by in corpus (3)

• Gorenstein homological algebra and universal coefficient theorems
• The spectrum of equivariant Kasparov theory for cyclic groups of prime order
• Filtrations in module categories, derived categories and prime spectra