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

TY - JOUR

T1 - Intermediate co-t-structures, two-term silting objects, τ-tilting modules, and torsion classes

AU - Iyama, Osamu

AU - Jørgensen, Peter

AU - Yang, Dong

N1 - Publisher Copyright: © 2014 Mathematical Sciences Publishers.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Co-t-structures

KW - Torsion classes

KW - Two-term silting objects

KW - τ-tilting modules

UR - https://www.scopus.com/pages/publications/84920930383

U2 - 10.2140/ant.2014.8.2413

DO - 10.2140/ant.2014.8.2413

M3 - Journal article

AN - SCOPUS:84920930383

SN - 1937-0652

VL - 8

SP - 2413

EP - 2431

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 10

ER -