Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stratification and duality for homotopical groups   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.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin