Stratification and duality for homotopical groups

Autor:	Barthel, Tobias, Castellana, Natalia, Heard, Drew, Valenzuela, Gabriel
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Topology Mathematics - Group Theory Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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 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. Comment: Corrected discussion of Chouinard's theorem for homotopical groups; accepted for publication in Advances in Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.03491 Zobrazit plný text záznamu View this record from Arxiv