On dense cohomological invariants

A classical theorem of Quillen expresses the mod-p cohomology of a finite group in terms of its elementary abelian p-subgroups, up to inseparable isogeny. In this talk I will discuss variations on this theme: “going pro-finite” and “going Mackey”. I will then explain how these are all linked to “dense invariants” in tensor-triangular geometry. Based on joint work with Paul Balmer.