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

TL;DR

This paper introduces a method to classify localizing subcategories in the bootstrap category of filtered C*-algebras using abelian approximation and noncrossing partitions, providing a comprehensive structural understanding.

Contribution

It offers a novel classification framework for localizing subcategories in filtered C*-algebras via lattice structures of noncrossing partitions.

Findings

Full classification of localizing subcategories achieved

Support notion for objects in the bootstrap category defined

Classification expressed through product of lattices of noncrossing partitions

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.