#### Vol. 3, No. 3, 2021

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A finiteness theorem for holonomic $\mathrm{DQ}$-modules on Poisson manifolds

### Masaki Kashiwara and Pierre Schapira

Vol. 3 (2021), No. 3, 571–588
##### Abstract

On a complex symplectic manifold, we prove a finiteness result for the global sections of solutions of holonomic $DQ$-modules in two cases: (a) by assuming that there exists a Poisson compactification, (b) in the algebraic case. This extends our previous result in which the symplectic manifold was compact. The main tool is a finiteness theorem for $ℝ$-constructible sheaves on a real analytic manifold in a nonproper situation.

##### Keywords
deformation quantization, holonomic modules, microlocal sheaf theory, constructible sheaves
##### Mathematical Subject Classification 2010
Primary: 53D55
Secondary: 19L10, 32C38, 35A27