Deformation quantization modules
Algebraic Geometry
2015-03-13 v3 K-Theory and Homology
Abstract
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.
Keywords
Cite
@article{arxiv.1003.3304,
title = {Deformation quantization modules},
author = {Masaki Kashiwara and Pierre Schapira},
journal= {arXiv preprint arXiv:1003.3304},
year = {2015}
}
Comments
This paper develops the results of Deformation quantization modules I (arXiv:0802.1245) and II (arXiv:0809.4309), and also contains new results and new remarks. It will appear in Asterisque, Soc. Math. France (2012)