Localising subcategories for cochains on the classifying space of a finite group

TL;DR

This paper classifies localising subcategories of the derived category of cochains on the classifying space of a finite group, establishing a correspondence with subsets of homogeneous prime ideals in the cohomology ring.

Contribution

It provides a complete classification of localising subcategories in this context, linking algebraic and topological structures.

Findings

Classification of localising subcategories

Correspondence with subsets of prime ideals

Insight into the structure of derived categories

Abstract

The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology ring $H^*(G,k)$.