Orbifold Cohomology as Periodic Cyclic Homology

DOI10.1142/S0129167X03001946zbMath1056.14028arXivmath/0206256MaRDI QIDQ4474442

Vladimir Baranovsky

Publication date: 12 July 2004

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0206256

zbMATH Keywords

derived categoriescrepant resolutionmixed complex

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Classical real and complex (co)homology in algebraic geometry (14F25) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Generalizations (algebraic spaces, stacks) (14A20)

Related Items

Compact hyper-Kähler categories, Poisson deformations of symplectic quotient singularities, Additive invariants of orbifolds, Brauer groups and crepant resolutions, The closed state space of affine Landau-Ginzburg B-models, Inner products of 2-representations, Equivariant Hodge theory and noncommutative geometry, Categorical Saito theory. II: Landau-Ginzburg orbifolds, Recent developments on noncommutative motives, The periodic cyclic homology of crossed products of finite type algebras, \(G\)-twisted braces and orbifold Landau-Ginzburg models, Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups, Formality of derived intersections and the orbifold HKR isomorphism, Categorical measures for finite group actions, Derived categories of Keum's fake projective planes

Cites Work

• Cyclic homology and equivariant theories
• The cyclic homology of the group rings
• On the Euler number of an orbifold
• Higher equivariant \(K\)-theory for finite group actions
• Equivalences of derived categories and \(K3\) surfaces
• On the cyclic homology of exact categories
• Cyclic cohomology of étale groupoids: The general case
• Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces
• Cyclic cohomology of crossed products by algebraic groups
• Equivariant sheaves and functors
• Cyclic cohomology of etale groupoids
• On Galois descent for Hochschild and cyclic homology
• The Hodge filtration and cyclic homology
• \(D\)-equivalence and \(K\)-equivalence
• Riemann-Roch theorems for Deligne-Mumford stacks
• The McKay correspondence as an equivalence of derived categories
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Deriving DG categories
• Equivariant cyclic homology and equivariant differential forms
• Cyclic homology for schemes