Structure of the Balmer spectrum of compact objects in Cell(G) for general finite groups

Determine the topology and structure of the Balmer spectrum Spc(Cell(G)c) of compact objects in the G-equivariant bootstrap tt-category Cell(G) for arbitrary finite groups G, beyond the special cases currently understood, to remove a key obstacle to establishing stratification more broadly.

Background

The authors compute Spc(Cell(G)c) in specific cases (e.g., groups where every nontrivial element has prime order) and rationally for all finite groups, but lack a general description for arbitrary finite groups.

They note that this gap in understanding Spc(Cell(G)c) is a major obstacle to proving stratification results for broader classes of finite groups.