三角范畴的粘合起源于 A. Grothendieck 的思想, 其公理化的定义由 A. A. Beilinson,J. N. Bernstein 和 P. Deligne 引入, 现已成为表示论和代数几何中的一个强有力工具.而三角范畴的ladder这一概念作为粘合的自然的推广，近些年来受到广泛关注.另一方面, Gorenstein同调代数是当前一种热门的相对同调代数，它的理论极其丰富，利用其理论可以为粘合(ladder)的存在性提供更多的依据。. 本课题的研究对象是Gorenstein导出范畴和Gorenstein奇点范畴间的粘合和ladder的存在性。我们希望找到Gorenstein导出范畴和Gorenstein奇点范畴间粘合存在的条件，并研究这些粘合何时能扩展为上下无界的ladder以及这些无界ladder的周期性。

The “gluing functors” was an observation of A. Grothendieck. The axiom of recollements of triangulated categories was given by A. A. Beilinson, J. N. Bernstein and P. Deligne. Now it has become a powerful tool in representation theory and algebraic geometry. In order to get more properties for triangulated categories, ladder was introduced. Ladder is a generalization of recollement. On the other hand, Gorenstein homological algebra is a popular area in homological algebras. It has fruitful results, which can give more evidences of the existences of recollements(ladders).. The research object of this proposal is the existences of the recollements (ladders) between the Gorenstein derived categories, and the Gorenstein singularity categories. We want to find the sufficient and necessary conditions for the existences, and study when these recollements can sit in unbounded ladders. We also study the periodicity of these unbounded ladders.