Quillen stratification in equivariant homotopy theory and higher representation theory

Tobias Barthel, Max Planck Institute of Mathematics

Online Talk

We prove a generalization of Quillen's stratification theorem in equivariant homotopy theory for a finite group working with arbitrary commutative equivariant ring spectra as coefficients, and suitably categorifying it via tensor-triangular geometry. We then apply our methods to the case of Borel-equivariant Lubin--Tate E-theory. In particular, this provides a computation of the Balmer spectrum as well as a cohomological parametrization of all localizing tensor-ideals of the category of equivariant modules over Lubin--Tate theory, thereby establishing a finite height analogue of the work of Benson, Iyengar, and Krause in modular representation theory. 

This is joint work with Natalia Castellana, Drew Heard, Niko Naumann, and Luca Pol.