We examine various triangulated quotients of the module category of a finite group. We demonstrate that these are not compactly generated by the simple modules and present a modification of Rickard's Idempotent Module construction that accounts for this. When the localizing subcategories are sufficiently nice we give an explicit description of the objects in the Bousfield triangles for modules that are direct limits of sequences of finite dimensional modules in terms of homotopy colimits.
From triangulated categories to module categories via homotopical algebra
Image-extension-closed subcategories of module categories of hereditary algebras
From triangulated categories to module categories via localisation
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