English

A correspondence and distance of t-structures

Representation Theory 2023-01-11 v2 Rings and Algebras

Abstract

For two t-structures D1=(D10,D11)D_{1}=(D_{1}^{\leqslant 0},D_{1}^{\geqslant 1}) and D2=(D20,D21)D_{2}=(D_{2}^{\leqslant 0},D_{2}^{\geqslant 1}) with D10D20D_{1}^{\leqslant 0} \subseteq D_{2}^{\leqslant 0} on a triangulated category D\mathcal{D}, we give a correspondence between t-structure Di=(Di0,Di1)D_{i}=(D_{i}^{\leqslant 0},D_{i}^{\geqslant 1}) which satisfies D10Di0D20D_{1}^{\leqslant 0} \subseteq D_{i}^{\leqslant 0} \subseteq D_{2}^{\leqslant 0} and a pair of full subcategories of D11D20D_{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 D1D_{1} whose heart H10H_{1} \neq 0 and that H1H_{1} has a non-trivial torsion pair, then for any integer nn, we can construct a t-structure D2D_{2} such that the distance between D1D_{1} and D2D_{2} is nn.

Keywords

Cite

@article{arxiv.2210.01541,
  title  = {A correspondence and distance of t-structures},
  author = {Junhua Zheng},
  journal= {arXiv preprint arXiv:2210.01541},
  year   = {2023}
}

Comments

13 pages. Any comments are welcome