Stacks of quantization-deformation modules on complex symplectic manifolds

Abstract

On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also quantize involutive submanifolds of contact manifolds.

In this new version, we have deleted from the previous one Lemma 7.6, Proposition 7.7 and Proposition 7.8 which were erroneous