Countable stratification of Cell(G) for all finite groups

Establish that the G-equivariant bootstrap tt-category Cell(G) is countably stratified for every finite group G, i.e., that the countable Balmer–Favi support induces a bijection between localizing×1 tensor ideals of Cell(G) and subsets of the Balmer spectrum Spc(Cell(G)c).

Background

The paper develops a countable analogue of Balmer–Favi supports suitable for categories admitting countable coproducts and proves stratification for several classes of finite groups, including those in which all nontrivial elements have prime order and rationally for all finite groups.

A general proof for arbitrary finite groups would classify localizing×1 tensor ideals of Cell(G) via subsets of Spc(Cell(G)c), completing the stratification program in this setting.