scholarly journals Silting Objects

2019 ◽  
Vol 51 (4) ◽  
pp. 658-690 ◽  
Author(s):  
Lidia Angeleri Hügel
Keyword(s):  
Silting Objects

scholarly journals Gluing Silting Objects

2014 ◽  
Vol 216 ◽  
pp. 117-151 ◽  
Author(s):  
Qunhua Liu ◽  
Jorge Vitória ◽  
Dong Yang
Keyword(s):  
Derived Category ◽  
The Other ◽  
Explicit Constructions ◽  
Other Hand ◽  
Silting Objects

AbstractRecent results by Keller and Nicolás and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and cot-structures with certain objects of the derived category: silting objects. On the other hand, the techniques of gluing (co-)t-structures along a recollement play an important role in the understanding of derived module categories. Using the above correspondence with silting objects, we present explicit constructions of gluing of silting objects, and, furthermore, we answer the question of when the glued silting is tilting.

scholarly journals Partial silting objects and smashing subcategories

2019 ◽  
Vol 296 (3-4) ◽  
pp. 887-900 ◽  
Author(s):  
Lidia Angeleri Hügel ◽  
Frederik Marks ◽  
Jorge Vitória
Keyword(s):  
Silting Objects

scholarly journals Discreteness of silting objects and t-structures in triangulated categories

2018 ◽  
Vol 118 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Takahide Adachi ◽  
Yuya Mizuno ◽  
Dong Yang
Keyword(s):  
Triangulated Categories ◽  
Silting Objects

Strong global dimensions of triangulated categories with respect to silting objects

2019 ◽  
Vol 47 (12) ◽  
pp. 5227-5239
Author(s):  
Qinghua Chen ◽  
Hongjin Liu
Keyword(s):  
Triangulated Categories ◽  
Silting Objects

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

2014 ◽  
Vol 8 (10) ◽  
pp. 2413-2431 ◽  
Author(s):  
Osamu Iyama ◽  
Peter Jørgensen ◽  
Dong Yang
Keyword(s):  
Tilting Modules ◽  
Silting Objects

scholarly journals Report on the finiteness of silting objects

2021 ◽  
pp. 1-17
Author(s):  
Takuma Aihara ◽  
Takahiro Honma ◽  
Kengo Miyamoto ◽  
Qi Wang
Keyword(s):  
Finite Algebra ◽  
Triangulated Categories ◽  
Finite Algebras ◽  
Silting Objects ◽  
Silting Object

Abstract We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, we study two classes of $\tau$ -tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when $\tau$ -tilting-finiteness implies representation-finiteness and obtain several classes of algebras in which a $\tau$ -tilting-finite algebra is representation-finite.

scholarly journals Lifting of recollements and gluing of partial silting sets

2021 ◽  
pp. 1-49
Author(s):  
Manuel Saorín ◽  
Alexandra Zvonareva
Keyword(s):  
Finite Length ◽  
Explicit Construction ◽  
Derived Categories ◽  
Triangulated Categories ◽  
Artin Algebras ◽  
Stable Categories ◽  
Silting Objects ◽  
Torsion Free

This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for a recollement of triangulated subcategories to lift to a torsion torsion-free triple (TTF triple) of ambient triangulated categories with coproducts is proved. As a consequence, lifting of TTF triples is possible for recollements of stable categories of repetitive algebras or self-injective finite length algebras and recollements of bounded derived categories of separated Noetherian schemes. When, in addition, the outer subcategories in the recollement are derived categories of small linear categories the conditions from the criterion are sufficient to lift the recollement to a recollement of ambient triangulated categories up to equivalence. In the second part we use these results to study the problem of constructing silting sets in the central category of a recollement generating the t-structure glued from the silting t-structures in the outer categories. In the case of a recollement of bounded derived categories of Artin algebras we provide an explicit construction for gluing classical silting objects.

scholarly journals Gluing Silting Objects

2014 ◽  
Vol 216 ◽  
pp. 117-151 ◽  
Author(s):  
Qunhua Liu ◽  
Jorge Vitória ◽  
Dong Yang
Keyword(s):  
Derived Category ◽  
The Other ◽  
Explicit Constructions ◽  
Other Hand ◽  
Silting Objects

AbstractRecent results by Keller and Nicolás and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and cot-structures with certain objects of the derived category: silting objects. On the other hand, the techniques of gluing (co-)t-structures along a recollement play an important role in the understanding of derived module categories. Using the above correspondence with silting objects, we present explicit constructions of gluing of silting objects, and, furthermore, we answer the question of when the glued silting is tilting.

scholarly journals From simple-minded collections to silting objects via Koszul duality

2018 ◽  
Vol 22 (1) ◽  
pp. 219-238 ◽  
Author(s):  
Hao Su ◽  
Dong Yang
Keyword(s):  
Koszul Duality ◽  
Silting Objects
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