Stratification and duality for homotopical groups
Abstract
We generalize Quillen's $F$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 $C^*(B\mathcal{G},\mathbb{F}_p)$ is stratified and costratified for a large class of $p$local compact groups $\mathcal{G}$ including compact Lie groups, connected $p$compact groups, and $p$local finite groups, thereby giving a supporttheoretic classification of all localizing and colocalizing subcategories of this category. Moreover, we prove that $p$compact groups admit a homotopical form of Gorenstein duality.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 arXiv:
 arXiv:1711.03491
 Bibcode:
 2017arXiv171103491B
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Group Theory;
 Mathematics  Representation Theory
 EPrint:
 Corrected discussion of Chouinard's theorem for homotopical groups