Homological and Commutative Algebra

Abstract

The purpose of these lectures is twofold. On the one hand, we shall study further the notion of satellites of functors in order to understand more generally what is going on in homological algebra. In particular, we shall try to see what happens if we consider functors defined on abelian categories when the domain category does not necessarily have projective or injective objects. Further, we shall investigate in what sense the notion of satellite still survives if we remove the condition that the domain and/or range of our functor is abelian.

Our second purpose is to look at concrete categories and see what the general methods of homological algebra yield in particular cases. More precisely, we shall look at the category of finitely generated modules over a local ring and, using ideas suggested by Ext, obtain some useful results some of which are directly connected with more classical problems.