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On Some Topological Properties of Fourier Transforms of Regular Holonomic ${\mathcal{D}}$-Modules

Part of: Singularities Analytic spaces Partial differential equations

Published online by Cambridge University Press:  06 January 2020

Yohei Ito  and
Kiyoshi Takeuchi
Yohei Ito
Affiliation:
Graduate School of Mathematical Science, The University of Tokyo, 3-8-1, Komaba, Meguro, Tokyo, 153-8914, Japan Email: yitoh@ms.u-tokyo.ac.jp
Kiyoshi Takeuchi
Affiliation:
Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan Email: takemicro@nifty.com
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Abstract

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We study Fourier transforms of regular holonomic ${\mathcal{D}}$-modules. In particular, we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic ${\mathcal{D}}$-modules will be given. Moreover, we give a new proof of the classical theorem of Brylinski and improve it by showing its converse.

Keywords

D-moduleFourier transformirregular singularity

MSC classification

Primary: 32C38: Sheaves of differential operators and their modules, $D$-modules
Secondary: 32S60: Stratifications; constructible sheaves; intersection cohomology 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 454 - 468
Copyright
© Canadian Mathematical Society 2019

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