论文标题
T结构的对应关系和距离
A correspondence and distance of t-structures
论文作者
论文摘要
对于两个t结构$ d_ {1} =（d_ {1}^{\ leqslant 0}，d_ {1}^{\ geqslant 1}）$和$ d_ {2} =（d_ {2}^{2}^{\ leqslant 0} $ d_ {1}^{\ leqslant 0} \ subseteq d_ {2}^{\ leqslant 0} $上的三角形类别$ \ mathcal {d} $ 0}，d_ {i}^{\ geqslant 1}）$，满足$ d_ {1}^{\ leqslant 0} \ subseteq d_ {i}^{\ leqslant 0} \ leqslant 0} \ subseteq d_ subseteq d_ {2}^2}^{2}^suiere $ d_ {1}^{\ geqslant 1} \ bigcap d_ {2}^{\ leqslant 0} $。然后，我们给出一种方法来确定两个T结构的距离，如果我们知道它们的距离是有限的。 $ d_ {1} $和$ d_ {2} $是$ n $。
For two t-structures $D_{1}=(D_{1}^{\leqslant 0},D_{1}^{\geqslant 1})$ and $D_{2}=(D_{2}^{\leqslant 0},D_{2}^{\geqslant 1})$ with $D_{1}^{\leqslant 0} \subseteq D_{2}^{\leqslant 0}$ on a triangulated category $\mathcal{D}$, we give a correspondence between t-structure $D_{i}=(D_{i}^{\leqslant 0},D_{i}^{\geqslant 1})$ which satisfies $D_{1}^{\leqslant 0} \subseteq D_{i}^{\leqslant 0} \subseteq D_{2}^{\leqslant 0}$ and a pair of full subcategories of $D_{1}^{\geqslant 1}\bigcap D_{2}^{\leqslant 0}$. Then we give a way to determine the distance of two t-structure if we have known that their distance is finite.In addition, if we set a t-structure $D_{1}$ whose heart $H_{1} \neq 0$ and that $H_{1}$ has a non-trivial torsion pair, then for any integer $n$, we can construct a t-structure $D_{2}$ such that the distance between $D_{1}$ and $D_{2}$ is $n$.
