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On some topological properties of Fourier transforms of regular holonomic \(\mathcal{D}\)-modules. (English) Zbl 1439.32025
Summary: 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.
MSC:
32C38 Sheaves of differential operators and their modules, \(D\)-modules
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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