On Serre duality for compact homologically smooth DG algebras

Abstract

The bounded derived category of coherent sheaves on a smooth projective variety is known to be equivalent to the triangulated category of perfect modules over a DG algebra. DG algebras, arising in this way, have to satisfy some compactness and smoothness conditions. In this paper, we describe a Serre functor on the category of perfect modules over an arbitrary compact and smooth DG algebra and use it to prove the existence of a non-degenerate pairing on the Hochschild homology of the DG algebra. This pairing is an algebraic analog of a well-known pairing on the Hodge cohomology of a smooth projective variety.

13 pages

References in corpus (5)

• Calabi-Yau algebras
• Lectures on Noncommutative Geometry
• On the cyclic homology of ringed spaces and schemes
• Generators and representability of functors in commutative and noncommutative geometry
• The Mukai pairing, I: the Hochschild structure

Cited by in corpus (9)

• Smoothness of equivariant derived categories
• A category of kernels for equivariant factorizations and its implications for Hodge theory
• Kaledin's degeneration theorem and topological Hochschild homology
• Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
• Calabi-Yau completions and orbifold equivalences
• Entropy of the composition of two spherical twists
• A category of kernels for equivariant factorizations, II: further implications
• Lefschetz type formulas for dg-categories
• Hirzebruch-Riemann-Roch for global matrix factorizations