t-结构与心的Recollement

t-Structure and Recollement of Hearts

设三角范畴D允许有关于三角范畴D′和D″的Recollement,给出D中t-结构能够诱导D′和D″的t-结构的充分必要条件.证明在一定条件下,D中t-结构的心允许有关于D′和D″的t-结构的心的Recollement,从而由已知三角范畴的Recollement构造若干Abel范畴的Recollement.

Let D,D ′ and D″ be triangulated categories.Suppose D admits a Recollement relative to D′ and D″.We give some necessary and sufficient criterions for a t-structrue on D inducing t-structures on D ′ and D″.Moreover,we take the advantage of the relationship between a t-structure on D and t-structures on D′ and D″ to show that the heart of the t-structure on D admits a Recollement relative to the other two hearts.Thus,we get a few Recollements of abelian categories according to a Recollement of triangulated categories.