2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131971We 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.To appear in the Proceedings of the Poisson 2006 (Tokyo), AMS Contemporary MathematicsQuantum AlgebraAlgebraic Geometry46L65, 14A20, 32C38, 53D55text