The global decomposition theorem for Hochschild (co-)homology of singular spaces via the Atiyah-Chern character

DOI10.1016/j.aim.2007.06.013zbMath1144.14015arXivmath/0606730OpenAlexW2089796676MaRDI QIDQ2461787

Hubert Flenner, Ragnar-Olaf Buchweitz

Publication date: 21 November 2007

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

Full work available at URL: https://arxiv.org/abs/math/0606730

zbMATH Keywords

Hochschild cohomologyHochschild homologyderived categoryAtiyah classperfect complexessemiregularityAtiyah-Chern character

Mathematics Subject Classification ID

Related Items (18)

Rigidity properties of the cotangent complex ⋮ Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes ⋮ Hodge theory and derived categories of cubic fourfolds ⋮ The characteristic morphism of an algebra ⋮ Homological mirror symmetry for Milnor fibers via moduli of A∞$A_\infty$‐structures ⋮ The K3 category of a cubic fourfold ⋮ Adjunctions and defects in Landau-Ginzburg models ⋮ Remarks on derived equivalences of Ricci-flat manifolds ⋮ When is the self-intersection of a subvariety a fibration? ⋮ Bivariance, Grothendieck duality and Hochschild homology. II: The fundamental class of a flat scheme-map ⋮ Dolbeault cohomologies of blowing up complex manifolds. II: Bundle-valued case ⋮ Derived equivalences of K3 surfaces and orientation ⋮ Derived geometry of the first formal neighbourhood of a smooth analytic cycle ⋮ Equivariant localization and completion in cyclic homology and derived loop spaces ⋮ Algèbres simplicialesS¹-équivariantes, théorie de de Rham et théorèmes HKR multiplicatifs ⋮ Hochschild (co-)homology of schemes with tilting object ⋮ Holomorphic Koszul-Brylinski homology via Dolbeault cohomology ⋮ Orbifold completion of defect bicategories

Cites Work

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• The Mukai pairing. II: The Hochschild-Kostant-Rosenberg isomorphism.
• The relative Riemann-Roch theorem from Hochschild homology
• Deformations and Fourier-Mukai transforms
• Hochschild cohomology of complex spaces and Noetherian schemes
• The decomposition of Hochschild cohomology and Gerstenhaber operations
• Hochschild cohomology of quasiprojective schemes
• Global Hochschild (co-)homology of singular spaces
• Rational homotopy theory
• Complexe cotangent et déformations. II
• Complex Analytic Connections in Fibre Bundles
• The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem
• The Trace Map and Characteristic Classes for Coherent Sheaves
• DEFORMATIONS OF COMPLEX SPACES
• Rozansky-Witten invariants via Atiyah classes

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