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A finiteness theorem
for holonomic $\mathrm{DQ}$-modules on Poisson manifolds
Masaki Kashiwara and Pierre Schapira |
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Vol. 3 (2021), No. 3, 571–588
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Abstract |
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On a complex symplectic manifold, we prove a finiteness result for the global sections of solutions of holonomic -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. |
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Keywords
deformation quantization, holonomic modules, microlocal
sheaf theory, constructible sheaves
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Mathematical Subject Classification 2010
Primary: 53D55
Secondary: 19L10, 32C38, 35A27
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Milestones
Received: 12 March 2020
Revised: 27 June 2020
Accepted: 12 July 2020
Published: 13 May 2021
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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 |
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