Localizing subcategories in the bootstrap category of filtered C*-algebras

Abstract

We use the abelian approximation for the bootstrap category of filtered C\*-algebras to define a sensible notion of support for its objects. As a consequence, we provide a full classification of localizing subcategories in terms of a product of lattices of noncrossing partitions of a regular $(n + 1)$gon, where $n$ is the number of ideals in the filtration.