Summer School 2001:
Homological conjectures for finite dimensional algebras

The lectures will deal with further connections of tilting theory and homologically finite subcategories. Most of the results presented here are based on joint work with Luise Unger.

One aspect will discuss the relationship of complements to partial tilting modules and the generalized Nakayama conjecture which was also investigated by Buan/Solberg. Reformulations in terms of homologically finite subcategories will be described.

Another aspect is the following open question: Under what conditions is a subcategory admitting a cocover already contravariantly finite. Trivial examples show that the answer is 'No' in general, but we will include various results showing that under certain extra assumptions the conclusion will hold.