Bousfield localization in quotients of module categories

Abstract

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.