Deformation quantization modules I:Finiteness and duality

Abstract

We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hslash ]$-modules on a topological space. Then we consider a $Z[\hslash ]$-algebra satisfying some suitable conditions and prove coherency results by using the property of being cohomologically complete. We apply these results to the study of modules over deformation quantization algebroids on complex Poisson manifolds. We prove in particular that under a natural properness condition, the convolution of two coherent kernels over such algebroids is coherent. We also construct the dualizing complexes in this framework and show that the convolution of kernels commutes with duality.

The contents of this paper is now included in Deformation quantization modules (arXiv:1003.3304).

References in corpus (4)

• Weak quantization of Poisson structures
• Regular holonomic D[[h]]-modules
• Deformation quantization modules II. Hochschild class
• An algebraic index theorem for Poisson manifolds

Cited by in corpus (9)

• A Localization Theorem for Finite W-algebras
• Twisted Deformation Quantization of Algebraic Varieties
• Regular holonomic D[[h]]-modules
• On Flatness and Completion for Infinitely Generated Modules over Noetherian Rings
• Projective module description of embedded noncommutative spaces
• Representation theory of the rational Cherednik algebras of type Z/lZ via microlocal analysis
• A noncommutative geometric approach to the quantum structure of spacetime
• Deformations of algebroid stacks
• Regularity for elliptic pairs over C[[h]]