#### Vol. 8, No. 10, 2014

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Intermediate co-$t$-structures, two-term silting objects, $\tau$-tilting modules, and torsion classes

### Osamu Iyama, Peter Jørgensen and Dong Yang

Vol. 8 (2014), No. 10, 2413–2431
##### Abstract

If $\left(A,B\right)$ and $\left({A}^{\prime },{B}^{\prime }\right)$ are co-$t$-structures of a triangulated category, then $\left({A}^{\prime },{B}^{\prime }\right)$ is called intermediate if $A\subseteq {A}^{\prime }\subseteq \Sigma A$. Our main results show that intermediate co-$t$-structures are in bijection with two-term silting subcategories, and also with support $\tau$-tilting subcategories under some assumptions. We also show that support $\tau$-tilting subcategories are in bijection with certain finitely generated torsion classes. These results generalise work by Adachi, Iyama, and Reiten.

##### Keywords
co-$t$-structures, two-term silting objects, $\tau$-tilting modules, torsion classes
Primary: 18E30
Secondary: 18E40
##### Milestones
Received: 7 December 2013
Revised: 13 October 2014
Accepted: 6 December 2014
Published: 31 December 2014
##### Authors
 Osamu Iyama Graduate School of Mathematics Nagoya University Chikusa-ku Nagoya, 464-8602 Japan Peter Jørgensen School of Mathematics and Statistics Newcastle University Newcastle upon Tyne NE1 7RU United Kingdom Dong Yang Department of Mathematics Nanjing University Nanjing, 210093 China