2024/09/24 by Kendall, Gregory
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2409.16094
openalex publication_date 2024/09/24 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28
In this work we construct a compactly generated tensor-triangulated stable category for a large class of infinite groups, including those in Kropholler's hierarchy LH\mathfrakF. This can be constructed as the homotopy category of a certain model category structure, which we show is Quillen equivalent to several other model categories, including those constructed by Bravo, Gillespie, and Hovey in their work on stable module categories for general rings. We also investigate the compact objects in this category. In particular, we give a characterisation of those groups of finite global Gorenstein AC-projective dimension such that the trivial representation ℤ is compact.