Colocalising subcategories of modules over finite group schemes

TL;DR

This paper classifies Hom closed colocalising subcategories of the stable module category for finite group schemes, using pi-points to identify key modules that generate and cogenerate these subcategories.

Contribution

It provides a classification of colocalising subcategories complementing previous work on localising subcategories, utilizing pi-points and endofinite modules.

Findings

Classification of Hom closed colocalising subcategories

Identification of endofinite modules associated with pi-points

Complementary to existing classification of localising subcategories

Abstract

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications involve pi-points in the sense of Friedlander and Pevtsova. We identify for each pi-point an endofinite module which both generates the corresponding minimal localising subcategory and cogenerates the corresponding minimal colocalising subcategory.