Mathematics – Quantum Algebra
Scientific paper
2008-02-09
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.
Kashiwara Masaki
Schapira Pierre
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