25 research outputs found
Stratification and duality for homotopical groups
We generalize Quillen's -isomorphism theorem, Quillen's stratification
theorem, the stable transfer, and the finite generation of cohomology rings
from finite groups to homotopical groups. As a consequence, we show that the
category of module spectra over is stratified
and costratified for a large class of -local compact groups
including compact Lie groups, connected -compact groups, and -local
finite groups, thereby giving a support-theoretic classification of all
localizing and colocalizing subcategories of this category. Moreover, we prove
that -compact groups admit a homotopical form of Gorenstein duality.Comment: Corrected discussion of Chouinard's theorem for homotopical groups;
accepted for publication in Advances in Mathematic