Summer School 2001:
Homological conjectures for finite dimensional algebras

In these lectures, we will define and study the unbounded derived category of the module category of an algebra. We will study its compactly generated (and, if time permits, its smashing) subcategories following Ravenel-Neeman (resp. Krause). In recent joint work, Beligiannis-Reiten have established a close link between this circle of ideas and the homological conjectures. Our aim will be to explain their results.