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* (BG, F-p) is stratified and costratified for a large class of p-local compact groups g 3 including compact Lie groups, connected p-compact ...
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* (BG, F-p) is stratified and costratified for a large class of p-local compact groups g 3 including compact Lie groups, connected p-compact groups, and p-local finite groups, thereby giving a support-theoretic classification of all localizing and colocalizing subcategories of this category. Moreover, we prove that p-compact groups admit a homotopical form of Gorenstein duality. (C) 2019 Elsevier Inc. All rights reserved.
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