Abstract

Tilting theory has originally been developed as a far reaching generalization of the Morita theory in the framework of finite dimensional representations of finite dimensional algebras. Some of the key aspects of the theory can however be extended to arbitrary modules over arbitrary rings. This is particularly important in the commutative setting, where finite dimensional tilting modules are trivial (projective). In the lecture series, we will present infinite dimensional tilting theory from the perspective of the approximation theory of modules. The key result making the theory manageable in this generality is the finite type of tilting classes, and hence their definability. We will also present several application, e.g., proving the finitistic dimension conjectures for (non-commutative) Iwanaga-Gorenstein rings. Finally, we will investigate the dual setting of cotilting classes in order to classify tilting classes in Mod-R (and hence the resolving subcategories of mod-R consisting of modules of bounded projective dimension) for any commutative noetherian ring R.

The series will consist of three lectures entitled:

Talk 1: Tilting modules and approximations,
Date and Time: Saturday, August 22 at 10:00-12:00

Talk 2: Finite type of tilting classes, and the finitistic dimension conjectures,
Date and Time: Sunday, August 23 at 10:00-12:00

Talk 3: Classification of tilting classes over commutative noetherian rings,
Date and Time: Monday, August 24 at 10:00-12:00



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