Deformation quantization modules

Details Deformation quantization modules Deformation quantization modules

2010-03-17

arxiv.org/abs/1003.3304v3

Mathematics

Algebraic Geometry

This paper develops the results of Deformation quantization modules I (arXiv:0802.1245) and II (arXiv:0809.4309), and also con

Scientific paper

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class commutes with composition of kernels, a kind of Riemann-Roch theorem in the non-commutative setting. Finally we study holonomic modules on complex symplectic manifolds and we prove in particular a constructibility theorem.

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