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

Published online by Cambridge University Press:  06 January 2020

Yohei Ito
Affiliation:
Graduate School of Mathematical Science, The University of Tokyo, 3-8-1, Komaba, Meguro, Tokyo, 153-8914, Japan Email: [email protected]
Kiyoshi Takeuchi
Affiliation:
Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan Email: [email protected]

Abstract

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.

Type
Article
Copyright
© Canadian Mathematical Society 2019

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