Intermediate co-t-structures, two-term silting objects, τ-tilting modules, and torsion classes

Iyama, Osamu; Jørgensen, Peter; Yang, Dong

doi:10.2140/ant.2014.8.2413

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

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

DOI: 10.2140/ant.2014.8.2413

Abstract

If $(A, B)$ and $(A^{'}, B^{'})$ are co- $t$ -structures of a triangulated category, then $(A^{'}, B^{'})$ is called intermediate if $A \subseteq A^{'} \subseteq Σ A$ . Our main results show that intermediate co- $t$ -structures are in bijection with two-term silting subcategories, and also with support $τ$ -tilting subcategories under some assumptions. We also show that support $τ$ -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

Mathematical Subject Classification 2010

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

Vol. 8, No. 10, 2014