Alperin's weight conjecture in terms of linear source modules and trivial source modules

We extend Knorr's and Robinson's reformulation of the blockwise version of Alperin's weight conjecture by showing that the alternating sum they introduced does not change its value if the terms which count simple modules are replaced by terms which count indecomposable linear source or trivial source modules. A more general result is established for quantities attached to finite groups admitting a defect group theory such that an analogue of Brauer's first main theorem or the Green correspondence holds.