Descent and Stratification in Equivariant Homotopy Theory
This is joint work with T. Barthel, D. Heard, N. Naumann, L. Pol. Quillen’s stratification theorem gives a geometric description of the cohomology of any finite group with coefficients in a field in terms of a decomposition of its Zariski spectrum into locally closed subsets indexed on the conjugacy classes of elementary abelian subgroups. In this project, we prove a version of this theorem in equivariant homotopy theory for a finite group, generalizing the classical theorem in two directions: we work with arbitrary commutative equivariant ring spectra as coefficients, and we categorify it to a result about equivariant modules. The result is formulated in the language of equivariant tensor-triangular geometry.