On the de Rham cohomology of differential and algebraic stacks

DOI10.1016/j.aim.2005.05.025zbMath1099.14007arXivmath/0410255OpenAlexW1983745776MaRDI QIDQ2577008

Kai A. Behrend

Publication date: 29 December 2005

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

Full work available at URL: https://arxiv.org/abs/math/0410255

zbMATH Keywords

spectral sequencesconnectionsgroupoidscotangent complexcofoliations

Mathematics Subject Classification ID

Deformation quantization, star products (53D55) de Rham cohomology and algebraic geometry (14F40) Pseudogroups and differentiable groupoids (58H05) Generalizations (algebraic spaces, stacks) (14A20)

Related Items

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras ⋮ Hodge theory of classifying stacks ⋮ Framed cohomological Hall algebras and cohomological stable envelopes ⋮ Multiplicative Ehresmann connections ⋮ Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable stacks ⋮ Equivariant Chow-Witt groups and moduli stacks of elliptic curves ⋮ Logarithmic quasimaps ⋮ Representations up to homotopy and Bott's spectral sequence for Lie groupoids ⋮ Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks ⋮ Equivariant cohomology for differentiable stacks ⋮ Toward an algebraic Donaldson-Floer theory ⋮ Sheaf theory for stacks in manifolds and twisted cohomology for \(S^1\)-gerbes ⋮ Absolute Chow-Künneth decomposition for rational homogeneous bundles and for log homogeneous varieties ⋮ Foliated groupoids and infinitesimal ideal systems ⋮ The ring structure for equivariant twisted K-theory ⋮ A note on the unirationality of a moduli space of double covers ⋮ Multiplicative forms and Spencer operators ⋮ Tangent curves to degenerating hypersurfaces ⋮ The Lusternik-Schnirelmann Category for a Differentiable Stack

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The equivariant Chern character for non-compact Lie groups
• The quantization conjecture revisited
• \(S^1\)-bundles and gerbes over differentiable stacks.
• Differential geometry of gerbes
• Simplicial homotopy theory
• Loop spaces, characteristic classes and geometric quantization