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 -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
Milestones
Received: 12 March 2020
Revised: 27 June 2020
Accepted: 12 July 2020
Published: 13 May 2021
Authors
Masaki Kashiwara
Research Institute for Mathematical Sciences
Kyoto University Institute for Advanced Study
Kyoto
Japan
Department of Mathematical Sciences and School of Mathematics
Korean Institute for Advanced Studies
Seoul
Korea
Pierre Schapira
Sorbonne Université, CNRS IMJ-PRG
Campus Pierre et Marie Curie
Paris
France