Mutations And Torsion Pairs Of The Presilting Subcategories In Triangulated Categories

Torsion pairs and mutations of torsion pairs are one of the forefront hot issues about algebra representation in triangulated categories, at the same time,presilting subcategory which is a new subcategory is proposed in triangulated categories.In this thesis, we are mainly focused on researching mutations and torsion pairs of the presilting subcategories.This master’s degree thesis consists of three chapters.In first chapter, we introduce some basic definitions, backgrounds needed in the sequel and the main results of this thesis.In second chapter, firstly, we present the concepts of silting,presilting,partial silting subcategory and the relations between them.Secondly,we give some definitions and results of new subcategory about the presilting subcatego-ry. Thirdly, we introduce the definition of D-presilting-mutation.Finally, we give the definitions of presilting mutations and equivalent characterizations between them.Meanwhile, we study some results about presilting mutations.In third chapter, we provide some concepts and properties about torsion pairs and the definitions of presilting torsion pairs and maximal presilting torsion pairs.Finally,we give the transformations between them and their e-quivalent characterizations.