Localization ans Support in Triangulated Categories

Specialeforsvar ved Rolf Christian Jørgensen

Titel: Localization and Support in Triangulated Categories

Abstract: We introduce and develop the basic theory of triangulated categories including a number of basic concepts, such as homological, cohomological and exact functors and triangulated subcategories. Among the basic results, we show that a right adjoint to an exact functor is exact. Next we discuss two approaches to localizations in triangulated categories. First we give a discussion of localization in a general categorical context and introduce a notion of a calculus of fractions for morphisms in a category which gives an accessible description of localization. We use this description of localization to define the Verdier quotient of a triangulated category by a triangulated subcategory. The second approach to localization which we discuss is Bousfield localization which is related to Verdier quotients through a question of existence of certain right adjoints. Finally we give a brief description of local cohomology functors and support in the context of triangulated categories.

Vejleder: Beren Sanders
Censor:   Niels Lauritzen, Aarhus Universitet