Support Varieties for Modular Representations

We present an overview of elementary methods to study extensions of modular representations of various types of "groups". We shall begin by discussing actions of an elementary abelian pp-group, E=(Z/p)rE=(Z/p)r, on finite dimensional vector spaces over a field kk of characteristic p>0p>0. This leads us to the broader study of the representations of a restricted Lie algebra gg on kk-vector spaces. We briefly mention how the questions raised and the techniques developed can be extended to modular representations of an arbitrary finite group scheme over kk. We then look more closely at the context of modular representations of an arbitrary finite group.