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

By Osamu Iyama, Peter Jørgensen, Dong Ping Yang. 2013

99 citations recorded by the source corpus.

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 \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 generalise results by Adachi, Iyama, and Reiten.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a5c9d337a642b2105abd2b293719dfb8487da172

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

Ordered Exchange Graphs (2013, background): “qq OO PP Ordered Exchange Graphs 45 The map 2-siltpΓq Ñ 2-siltpJq was deﬁned in Theorem 4.4. 2-siltpΓq ÝÑ sτ-tiltpJq: This map is deﬁned as taking the 0-th cohomology: MÞÑH0pMq “ Hom perpΓqpΓ,Mq, see [53]. 2-siltpJq ÝÑ sτ-tiltpJq: This map is deﬁned as taking the 0-th cohomology: M ÞÑH0pMq “ Hom Hbp”
Classifying tilting complexes over preprojective algebras of Dynkin type (2015, background): “MR Zbl [Iyama et al. 2014] O. Iyama, P. Jørgensen, and D. Yang, “Intermediate co-t-structures, two-term silting objects, τ -tilting modules, and torsion classes”, Algebra Number Theory 8:10 (2014), 2413– 2431.”