Natalia Castellana Vila: Quillen stratification in equivariant homotopy theory

Abstract.

Quillen's stratification theorem describes the spectrum of prime ideals of the mod \(p\) cohomology of a finite group in terms of the corresponding spectrum for the familiy of elementary abelian \(p\)-subgroups. In this paper 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, in the context of via tensor-triangular geometry and the Balmer spectrum. We describe the case of Borel-equivariant Lubin–Tate E-theory. In particular, this provides a computation of the Balmer spectrum and a classification of all localizing tensor-ideals of the category of equivariant modules over Lubin–Tate theory. This is joint work with Tobias Barthel, Drew Heard, Niko Naumann, and Luca Pol.