The HRS tilting process and Grothendieck hearts of t-structures

DOI10.1090/conm/769/15416zbMath1497.18010arXiv2001.08638OpenAlexW3159718075MaRDI QIDQ5043424

Manuel Saorín, Carlos E. Parra

Publication date: 21 October 2022

Published in: Representations of Algebras, Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.08638

zbMATH Keywords

derived categoryGrothendieck categorytorsion pairt-structureheart of a t-structureHappel-Reiten-Smalø t-structure

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Torsion theories, radicals (18E40) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Abelian categories, Grothendieck categories (18E10) Derived categories and associative algebras (16E35) Derived categories, triangulated categories (18G80)

Related Items (4)

Local coherence of hearts associated with Thomason filtrations ⋮ Locally finitely presented and coherent hearts ⋮ Tilting preenvelopes and cotilting precovers in general abelian categories ⋮ Reflective and coreflective subcategories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the heart associated with a torsion pair
• When the heart of a faithful torsion pair is a module category
• Definability and approximations in triangulated categories
• On the heart of a faithful torsion theory
• Addendum to ``Direct limits in the heart of a t-structure: the case of a torsion pair
• Brown representability does not come for free
• Quasi-tilting modules and counter equivalences
• Silting theory in triangulated categories with coproducts
• Exactness of direct limits for abelian categories with an injective cogenerator
• Derivators, pointed derivators and stable derivators
• Pure projective tilting modules
• Purity in compactly generated derivators and t-structures with Grothendieck hearts
• Cotilting sheaves on Noetherian schemes
• \( \infty \)-tilting theory
• Derived equivalences via HRS-tilting
• Direct limits in the heart of a t-structure: the case of a torsion pair
• Torsion pairs in silting theory
• Sur quelques points d'algèbre homologique
• Triangulated Categories
• Tilting objects in abelian categories and quasitilted rings
• The 𝑡-structure induced by an 𝑛-tilting module
• Tilting in abelian categories and quasitilted algebras
• Weight Structures and Simple dg Modules for Positive dg Algebras
• Hearts of t-structures in the derived category of a commutative Noetherian ring

This page was built for publication: The HRS tilting process and Grothendieck hearts of t-structures