Torsion Endotrivial Modules

Abstract

We discuss the tedious problem of finding all (indecomposable) trivial source endotrivial modules for a finite group. The Green correspondence does not suffice in general and several ingenious methods have been devised to answer this question: using ordinary character theory, methods derived from algebraic geometry, and methods using homotopy theory. We present each of these and give a few examples of their successful applications.