A correspondence and distance of t-structures

Junhua Zheng

paper

A correspondence and distance of t-structures

arXiv:2210.01541

Abstract

For two t-structures $D_{1} = (D_{1}^{⩽ 0}, D_{1}^{⩾ 1})$ and $D_{2} = (D_{2}^{⩽ 0}, D_{2}^{⩾ 1})$ with $D_{1}^{⩽ 0} \subseteq D_{2}^{⩽ 0}$ on a triangulated category $D$ , we give a correspondence between t-structure $D_{i} = (D_{i}^{⩽ 0}, D_{i}^{⩾ 1})$ which satisfies $D_{1}^{⩽ 0} \subseteq D_{i}^{⩽ 0} \subseteq D_{2}^{⩽ 0}$ and a pair of full subcategories of $D_{1}^{⩾ 1} ⋂ D_{2}^{⩽ 0}$ . 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 $n$ .

13 pages. Any comments are welcome