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

If (A,B) and (A,B) are co-t-structures of a triangulated category, then (A,B) is called intermediate if A A ΣA. 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.

co-$t$-structures, two-term silting objects, $\tau$-tilting modules, torsion classes
Mathematical Subject Classification 2010
Primary: 18E30
Secondary: 18E40
Received: 7 December 2013
Revised: 13 October 2014
Accepted: 6 December 2014
Published: 31 December 2014
Osamu Iyama
Graduate School of Mathematics
Nagoya University Chikusa-ku
Nagoya, 464-8602
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