Colocalising subcategories of modules over finite group schemes

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.