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- Title
On the Picard Group of the Stable Module Category for Infinite Groups.
- Authors
Gómez, Juan Omar
- Abstract
We introduce the stable module |$\infty $| -category for groups of type |$\Phi $| as an enhancement of the stable category defined by N. Mazza and P. Symonds. For groups of type |$\Phi $| that act on a tree, we show that the stable module |$\infty $| -category decomposes in terms of the associated graph of groups. For groups that admit a finite-dimensional cocompact model for the classifying space for proper actions, we exhibit a decomposition in terms of the stable module |$\infty $| -categories of their finite subgroups. We use these decompositions to provide methods to compute the Picard group of the stable module category. In particular, we provide a description of the Picard group for countable locally finite |$p$| -groups.
- Subjects
PICARD groups; INFINITE groups; DECOMPOSITION method; TREES
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 16, p11514
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnae125