Relative singularity categories and Gorenstein-projective modules

DOI10.1002/mana.200810017zbMath1244.18014arXiv0709.1762OpenAlexW2083749578MaRDI QIDQ3082484

Xiao-Wu Chen

Publication date: 10 March 2011

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.1762

zbMATH Keywords

Gorenstein-projective modulesrelative singularity categorycompact objectsGorenstein local ringsmCM-modulesrelative CM-modules

Mathematics Subject Classification ID

Relative homological algebra, projective classes (category-theoretic aspects) (18G25) Chain complexes (category-theoretic aspects), dg categories (18G35) Derived categories and associative algebras (16E35)

Related Items (39)

Applications of balanced pairs ⋮ Relative singularity categories. I: Auslander resolutions. ⋮ Zaks' lemma for coherent rings. ⋮ Triangulated equivalence between a homotopy category and a triangulated quotient category ⋮ Singular equivalences induced by homological epimorphisms ⋮ Derived representation type and Gorenstein projective modules of an algebra under crossed product. ⋮ Exact categories, big Cohen-Macaulay modules and finite representation type ⋮ Frobenius functors and Gorenstein homological properties ⋮ Totally acyclic complexes over noetherian schemes ⋮ Relative singularity categories with respect to Gorenstein flat modules ⋮ Relative derived categories, relative singularity categories and relative defect categories ⋮ Change of rings and singularity categories ⋮ The dg Leavitt algebra, singular Yoneda category and singularity category ⋮ Homological epimorphisms, compactly generated \(t\)-structures and Gorenstein-projective modules ⋮ Gorenstein projective modules and recollements over triangular matrix rings ⋮ The relative singularity category of a non-commutative resolution of singularities ⋮ Compact generators in categories of matrix factorizations ⋮ On singular equivalences of Morita type ⋮ Unnamed Item ⋮ Relative singularity categories. II ⋮ Algebras with radical square zero are either self-injective or CM-free ⋮ Three results on Frobenius categories ⋮ Pure derived and pure singularity categories ⋮ Gorenstein projective and injective dimensions over Frobenius extensions ⋮ An Auslander-type result for Gorenstein-projective modules. ⋮ Relative singularity categories and singular equivalences ⋮ Relative singularity categories, Gorenstein objects and silting theory ⋮ Gorenstein singularity categories ⋮ On the recollements of functor categories ⋮ Triangle equivalences involving Gorenstein FP-injective modules ⋮ On triangle equivalences of stable categories ⋮ Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements ⋮ A note on equivariantization of additive categories and triangulated categories ⋮ Buchweitz’s equivalences for Gorenstein flat modules with respect to semidualizing modules ⋮ When the Schur functor induces a triangle-equivalence between Gorenstein defect categories ⋮ Frobenius functors, stable equivalences and \(K\)-theory of Gorenstein projective modules ⋮ Relative global dimensions and stable homotopy categories ⋮ The singularity category of a Nakayama algebra. ⋮ Relative singularity categories

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