Relative singularity categories. I: Auslander resolutions.

DOI10.1016/j.aim.2016.06.011zbMath1348.14009arXiv1205.1008OpenAlexW2099387327MaRDI QIDQ305751

Dong Yang, Martin Kalck

Publication date: 30 August 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1008

zbMATH Keywords

Gorenstein algebraDynkin diagramsisolated singularityrecollementsingularity categoryADE singularitiescomplete path algebradg Auslander algebraGorenstein singularitynon-commutative resolutionperfect sheavesrelative singularity category

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15)

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Uses Software

• classifyCeq.lib

Cites Work

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• Relative singularity categories. I: Auslander resolutions.
• The relative singularity category of a non-commutative resolution of singularities
• Maximal modifications and Auslander-Reiten duality for non-isolated singularities
• Explicit models for some stable categories of maximal Cohen-Macaulay modules
• Cluster tilting objects in generalized higher cluster categories.
• Unifying two results of Orlov on singularity categories
• Formal completions and idempotent completions of triangulated categories of singularities
• Derived equivalences from mutations of quivers with potential
• The ubiquity of generalized cluster categories
• Braid groups and Kleinian singularities
• Three-dimensional flops and noncommutative rings
• Parametrizing recollement data for triangulated categories
• Simple singularities in positive characteristic
• Cluster categories for algebras of global dimension 2 and quivers with potential.
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander correspondence.
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• Lefschetz decompositions and categorical resolutions of singularities
• Partial flag varieties and preprojective algebras.
• Koszul equivalences in \(A_\infty\)-algebras.
• Categorical resolution of singularities
• Hochschild cohomology and stratifying ideals.
• Grothendieck group and generalized mutation rule for 2-Calabi-Yau triangulated categories
• Algebren, Darstellungsköcher, Überlagerungen und zurück
• Localization of triangulated categories and derived categories
• Rings mit only finitely many isomorphism classes of maximal indecomposable Cohen-Macaulay modules
• The derived equivalence classification of representation-finite selfinjective algebras
• Matrix factorizations over projective schemes
• Reflexive modules on quotient surface singularities
• Cohen-Macaulay modules on hypersurface singularities. I
• Braid group actions on derived categories of coherent sheaves.
• A new triangulated category for rational surface singularities
• Kleinian singularities, derived categories and Hall algebras
• Formality of DG algebras (after Kaledin)
• Non-commutative resolutions and Grothendieck groups
• Calabi-Yau algebras and superpotentials
• Coherent analogues of matrix factorizations and relative singularity categories
• Compact corigid objects in triangulated categories and co-\(t\)-structures
• Negative \(K\)-theory of derived categories
• Sur les ordres commutatifs avec un nombre fini de réseaux indecomposables
• Triangulated Categories
• The McKay correspondence as an equivalence of derived categories
• Noetherian hereditary abelian categories satisfying Serre duality
• Derived equivalences for Φ-Auslander-Yoneda algebras
• Preprojective algebras and c -sortable words
• Reconstruction algebras of type 𝐴
• Weight structures vs.t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)
• Relative singularity categories and Gorenstein-projective modules
• Cluster structures for 2-Calabi–Yau categories and unipotent groups
• Triangulated categories of singularities and equivalences between Landau-Ginzburg models
• On the structure of triangulated categories with finitely many indecomposables
• Stability Conditions and Kleinian Singularities
• ON THE HOMOLOGY THEORY OF FIBRE SPACES
• Rational Singularities and Almost Split Sequences
• The Auslander-Reiten Quiver of a Simple Curve Singularity
• Hypersurface Singularities of Finite Cohen-Macaulay Type
• Deriving DG categories
• Silting reduction and Calabi–Yau reduction of triangulated categories
• Derived Equivalences As Derived Functors
• Frobenius categories, Gorenstein algebras and rational surface singularities
• Stable categories of Cohen-Macaulay modules and cluster categories: Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday
• The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
• On Generalized Cluster Categories
• COMMUTATIVE RINGS WITH A FINITE NUMBER OF INDECOMPOSABLE INTEGRAL REPRESENTATIONS
• Des catégories abéliennes
• Stratifying endomorphism algebras
• Idempotent completion of triangulated categories
• On \(t\)-structures and torsion theories induced by compact objects