Singular equivalences to locally coherent hearts of commutative Noetherian rings

DOI10.1016/j.jalgebra.2023.05.022arXiv2109.13853OpenAlexW3204395970MaRDI QIDQ6169104

Sergio Pavon, Michal Hrbek

Publication date: 11 July 2023

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

Full work available at URL: https://arxiv.org/abs/2109.13853

zbMATH Keywords

homotopy categoryderived categorylocally coherent categorycoderived categorycotilting complexKrause recollement

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Resolutions; derived functors (category-theoretic aspects) (18G10) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

Cites Work

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• Approximations and adjoints in homotopy categories
• On locally coherent hearts
• On exact categories and applications to triangulated adjoints and model structures
• The spectrum of a locally coherent category
• Pseudo-dualizing complexes and pseudo-derived categories
• Compactly generated \(t\)-structures on the derived category of a noetherian ring
• Commutative coherent rings
• Silting and cosilting classes in derived categories
• Categorical resolutions of a class of derived categories
• Silting theory in triangulated categories with coproducts
• Realisation functors in tilting theory
• Resolution of unbounded complexes in Grothendieck categories
• Derivators, pointed derivators and stable derivators
• Relative homological algebra and purity in triangulated categories
• Hearts for commutative Noetherian rings: torsion pairs and derived equivalences
• Compactly generated t-structures in the derived category of a commutative ring
• Purity in compactly generated derivators and t-structures with Grothendieck hearts
• Telescope conjecture for homotopically smashing t-structures over commutative Noetherian rings
• Models for singularity categories.
• Singular derived categories of \(\mathbb{Q}\)-factorial terminalizations and maximal modification algebras
• Derived equivalences induced by big cotilting modules
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• Compact objects in stable module categories.
• Localization theory for triangulated categories
• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• DERIVED FUNCTORS OF INVERSE LIMITS REVISITED
• Triangulated categories of singularities and equivalences between Landau-Ginzburg models
• Classifying finite localizations of quasicoherent sheaves
• Locally finitely presented additive categories
• The Ziegler Spectrum of a Locally Coherent Grothendieck Category
• The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
• Flat ring epimorphisms and universal localizations of commutative rings
• Models for homotopy categories of injectives and Gorenstein injectives
• The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
• Tilting, cotilting, and spectra of commutative noetherian rings
• Categories and Sheaves
• Some Results on Coherent Rings
• the stable derived category of a noetherian scheme
• Lifting and restricting t‐structures