由Recollement导出的t-结构的非退化性和有界性

根据Beilinson A,Bernstein J,Deligne P的结论可知,若三个三角范畴允许有一个Recollement,则Recollement两端三角范畴上的t-结构可以诱导中间三角范畴上的一个t-结构.在这篇文章中讨论了这三个t-结构在非退化性和有界性上的联系.首先证明了两端三角范畴上的t-结构是非退化的当且仅当中间三角范畴上的t-结构是非退化的.其次证明了两端三角范畴上的t-结构是有界的当且仅当中间三角范畴上的t-结构是有界的.最后讨论了Recollement函子的t-正合性.

Nondegeneration and Boundedness of t-structure Induced by Recollement

According to the conclusion of Beilinson A, Bernstein J, Deligne P,if there is a Recollement about three triangulated categories,the t-structures on the triangulated categories of the both ends of the Recollement can induce a t-structure on the middle one. In this paper,we mainly discuss the relations among three t-structures on nondegeneration and boundedness was discussed. First,it is showed that the t-structures on both ends are nondegenerate if and only if the t-structure on middle is nondegenerate. Second, it is proved that the t-structures on both ends are bounded if and only if the t-structure on middle is bounded. Finelly some t-exact properties of the functors in a Recollement were discussed.