REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: The category of modules over any non-commutative ring can be recovered through four different Serre localizations of common functor categories, two of which consist of contravariant functors and two of which consist of covariant functors. In this talk I will describe the relationship between these four functor categories and their respective localization functors. I will present applications of the Auslander-Gruson-Jensen functor which is an exact contravariant functor sending representable functors to tensor functors. In particular, the Auslander-Gruson-Jensen functor induces a duality between the Serre subcategories of injectively stable covariant finitely presented functors and projectively stable contravariant finitely presented functors. This duality can be used to recover the Auslander-Reiten formulas. This talk will discuss results from joint work with Samuel Dean and separately results from joint work with Alex Martsinkovsky.