Deformation quantization modules on complex symplectic manifolds

Pierre Schapira

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arXiv · 0704.3007

Deformation quantization modules on complex symplectic manifolds

Pierre Schapira

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Abstract

We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along smooth Lagrangian submanifolds, perversity of the complex of solutions for regular holonomic $\W[\stx]$-modules, finiteness and duality for the composition of ``good'' kernels. As a corollary, we get that the derived category of good $\W[\stx]$-modules with compact support is a Calabi-Yau category. We also give a conjectural Riemann-Roch type formula in this framework.

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BibTeX RIS

Pierre Schapira. 2007-06-20. Deformation quantization modules on complex symplectic manifolds. https://arxiv.org/abs/0704.3007

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