Noncommutative crepant resolutions, an overview

DOI10.4171/icm2022/177arXiv2207.09703OpenAlexW4389775903MaRDI QIDQ6198724

Michel Van den Bergh

Publication date: 20 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.09703

zbMATH Keywords

quotient singularitiestilting objectsnoncommutative crepant resolutions

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Minimal model program (Mori theory, extremal rays) (14E30) Derived categories, triangulated categories (18G80)

Cites Work

• Derived categories of toric varieties. III
• Autoequivalences of derived categories via geometric invariant theory
• Derived categories of Grassmannians over integers and modular representation theory
• Properly ordered dimers, \(R\)-charges, and an efficient inverse algorithm
• Maximal modifications and Auslander-Reiten duality for non-isolated singularities
• Tilting bundles on rational surfaces and quasi-hereditary algebras
• Derived equivalences from mutations of quivers with potential
• Three-dimensional flops and noncommutative rings
• Non-commutative crepant resolutions for some toric singularities. II
• Induced nilpotent orbits and birational geometry
• Noncommutative resolutions and rational singularities
• Mellin--Barnes integrals as Fourier--Mukai transforms
• Dimer models and the special McKay correspondence
• Lefschetz decompositions and categorical resolutions of singularities
• Derived categories of quadric fibrations and intersections of quadrics
• Flops connect minimal models
• Remarks on non-commutative crepant resolutions of complete intersections
• Categorical resolution of singularities
• Helices on del Pezzo surfaces and tilting Calabi-Yau algebras
• Non-commutative desingularization of determinantal varieties. I
• Quivers with potentials and their representations. I: Mutations.
• Cyclic homology, derivations, and the free loopspace
• Über die Glattheit von Quotientenabbildungen. (On the smoothness of quotient maps)
• Partial desingularisations of quotients of nonsingular varieties and their Betti numbers
• A formal inverse to the Cayley-Hamilton theorem
• On the derived categories of coherent sheaves on some homogeneous spaces
• Regularity of trace rings of generic matrices
• Stability and equivariant maps
• Coherent sheaves on \({\mathbb{P}}^n\) and problems of linear algebra
• Cohen-Macaulayness of modules of covariants
• The invariant theory of \(n\times n\) matrices
• Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
• Germs of arcs on singular algebraic varieties and motivic integration
• On the cyclic homology of exact categories
• Local cohomology of modules of covariants
• \(D\)-equivalence and \(K\)-equivalence
• Stringy Hodge numbers and Virasoro algebra
• Flops and derived categories.
• Non-commutative resolutions of quotient singularities for reductive groups
• Flops and clusters in the homological minimal model programme
• Variation of geometric invariant theory quotients and derived categories
• Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities.
• Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
• Symplectic singularities
• On the Abuaf-Ueda flop via non-commutative crepant resolutions
• Canonical reduction of stabilizers for Artin stacks with good moduli spaces
• Motivic zeta functions on \(\mathbb{Q}\)-Gorenstein varieties
• Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration
• Tilting preserves finite global dimension
• Stability conditions and the \(A_2\) quiver
• Perverse schobers on Riemann surfaces: constructions and examples
• Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups
• Hori-mological projective duality
• Cluster equivalence and graded derived equivalence.
• Calabi-Yau algebras and superpotentials
• Localization of modules for a semisimple Lie algebra in prime characteristic (with an appendix by R. Bezrukavnikov and S. Riche, Computation for \(\text{sl}(3))\)
• Perverse schobers and birational geometry
• On stringy Euler characteristics of Clifford non-commutative varieties
• Derived equivalences by quantization
• Singular derived categories of \(\mathbb{Q}\)-factorial terminalizations and maximal modification algebras
• Homological projective duality
• On Azumaya algebras and finite dimensional representations of rings
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• The McKay correspondence as an equivalence of derived categories
• On crepant resolution of some hypersurface singularities and a criterion for UFD
• Stability conditions for Slodowy slices and real variations of stability
• On the noncommutative Bondal–Orlov conjecture
• Window shifts, flop equivalences and Grassmannian twists
• Some New Examples of Nondegenerate Quiver Potentials
• Non-commutative crepant resolutions: scenes from categorical geometry
• On the derived category of Grassmannians in arbitrary characteristic
• REPRESENTATION OF ASSOCIATIVE ALGEBRAS AND COHERENT SHEAVES
• Dimer models and Calabi-Yau algebras
• The orbifold Chow ring of toric Deligne-Mumford stacks
• Combinatorial constructions of derived equivalences
• Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
• Hodge theoretic aspects of mirror symmetry
• Existence of minimal models for varieties of log general type
• Morita Theory for Derived Categories
• Flops
• Trace rings of generic 2 by 2 matrices
• Quiver Concomitants are Often Reflexive Azumaya
• Cohen-Macaulayness of Semi-Invariants for Tori
• A Converse to Stanley's Conjecture for Sl 2
• Non-commutative Desingularization of Determinantal Varieties, II: Arbitrary Minors
• The stringy E-function of the moduli space of rank 2 bundles over a Riemann surface of genus 3
• Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions
• Gorenstein modifications and \mathds{𝑄}-Gorenstein rings
• [https://portal.mardi4nfdi.de/wiki/Publication:5204036 Stringy $E$-functions of Pfaffian�Grassmannian double mirrors]
• The derived category of a GIT quotient
• Categorical Resolutions of Irrational Singularities
• The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
• Sur les modules de covariants
• Fedosov quantization in positive characteristic
• Non-Commutative Crepant Resolutions for Some Toric Singularities I
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