Studying On The Compactness And Gorenstein Of T-structures Induced By Recollement

In the past forty five years,the theory and the use of triangulated categories has en-joyed a vigorous development.Since 1965,the relative homological algebra,especially the Gorenstein homological algebra has been developed to an advanced level.This thesis for M.Sc.degree is to study the compactly generated t-structure of a ladder and a ladder of Gorenstein module.The main results obtained are follows:In the first section of chapter 3,given a recollement(τ’,τ,τ’’,i*,i’,j1,j*,j*),where τ’,τ,τ" are triangulated categories with small coproducts and T is compactly generated.Among the others,we(1)show the BBD-induction of compactly generated t-structures is compactly gener-ated when i*preserves compact objects;(2)give a ladder(τ’,τ,τ",τ,τ’)of height 2.Then the certain BBD-induction of compactly generated t-structures is compactly generated.In the second section of chapter 3,we show that a recollement of derived categories of algebras induced by some homological ring epimorphism produces a ladder of the stable categories of Gorenstein-projective modules over corresponding algebras.