Barthel, Tobias and Castellana, Natalia and Heard, Drew and Valenzuela, Gabriel (2019) Stratification and duality for homotopical groups. ADVANCES IN MATHEMATICS, 354: 106733. ISSN 0001-8708, 1090-2082
Full text not available from this repository. (Request a copy)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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | P-COMPACT GROUPS; COHOMOLOGY RINGS; CLASSIFYING-SPACES; LOCAL COHOMOLOGY; FUSION SYSTEMS; FINITE-GROUPS; LIE-GROUPS; LOCALIZATION; UNIQUENESS; REPRESENTATION; p-local compact groups; Support theory; F-isomorphism theorem; Stratification and costratification; Gorenstein duality |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Niko Naumann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Mar 2020 06:48 |
| Last Modified: | 06 Apr 2020 06:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26191 |
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