We prove a variant 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. 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 Tobias Barthel, Natalia Castellana, Drew Heard and Luca Pol, and related to this arXiv paper.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
