Deformation quantization modules I:Finiteness and duality

Details Deformation quantization modules I:Finiteness and duality Deformation quantization modules I:Finiteness and duality

2008-02-09

arxiv.org/abs/0802.1245v4

Mathematics

Quantum Algebra

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

Scientific paper

We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-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.

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