Title: A green way to locally source indecomposable modules
Abstract: The representation theory of a finite group G, over a field k of characteristic not dividing the order, is well understood and relies solely on classifying the finite list of simple modules. In the modular case simple and indecomposable no longer coincide and the list of indecomposables may not be finite. How does one even begin to classify the indecomposables? One approach is to do so locally. We will attempt to prove the Green correspondence, which gives a correspondence between the indecomposables of G and the indecomposables of its p-local subgroups. This provides a local-to-global approach to studying the representation theory of G by its p-subgroups which, often, have simpler representation theory.