Silting and cosilting classes in derived categories

DOI10.1016/J.JALGEBRA.2017.12.031zbMath1441.16011arXiv1704.06484OpenAlexW2963148052MaRDI QIDQ1703233

Jorge Vitória, Frederik Marks

Publication date: 1 March 2018

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06484

zbMATH Keywords

derived categorysilting complextorsion pairt-structureco-t-structurecosilting complex

Mathematics Subject Classification ID

Torsion theories, radicals (18E40) Derived categories and associative algebras (16E35) Derived categories, triangulated categories (18G80)

Related Items (17)

Silting and cosilting modules over trivial ring extensions ⋮ Compactly generated t-structures in the derived category of a commutative ring ⋮ Weight structures cogenerated by weak cocompact objects ⋮ Injective cogenerators, cotilting modules and cosilting modules ⋮ Lifting and restricting t‐structures ⋮ Purity in compactly generated derivators and t-structures with Grothendieck hearts ⋮ The structure of aisles and co-aisles of t-structures and co-t-structures ⋮ Singular equivalences to locally coherent hearts of commutative Noetherian rings ⋮ \(t\)-structures on stable derivators and Grothendieck hearts ⋮ Telescope conjecture for homotopically smashing t-structures over commutative Noetherian rings ⋮ Unnamed Item ⋮ An Auslander-Buchweitz approximation approach to (pre)silting subcategories in triangulated categories ⋮ Definable coaisles over rings of weak global dimension at most one ⋮ Hearts for commutative Noetherian rings: torsion pairs and derived equivalences ⋮ Silting Objects ⋮ Definability and approximations in triangulated categories ⋮ Parametrizing torsion pairs in derived categories

Cites Work

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• Semi-tilting complexes.
• Smashing subcategories and the telescope conjecture -- an algebraic approach
• Relative homological algebra and purity in triangulated categories
• When are definable classes tilting and cotilting classes?
• Cosilting complexes and AIR-cotilting modules
• Torsion pairs in silting theory
• Silting objects, simple-minded collections, \(t\)-structures and co-\(t\)-structures for finite-dimensional algebras.
• Approximations and endomorphism algebras of modules.
• Infinitely generated complements to partial tilting modules
• On compactly generated torsion pairs and the classification of co-$t$-structures for commutative noetherian rings
• Silting Modules
• Silting mutation in triangulated categories
• All 𝑛-cotilting modules are pure-injective
• Cotilting modules are pure-injective
• Silting Modules over Commutative Rings
• The Tilting–Cotilting Correspondence
• On the abundance of silting modules
• All tilting modules are of finite type
• Cotilting and tilting modules over Prüfer domains
• Tilting modules and Gorenstein rings
• Homological and homotopical aspects of torsion theories

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