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- Title
- Enhanced Nearby and Vanishing Cycles in Dimension One and Fourier Transform
- KIAS Author
- Kashiwara, Masaki
- Journal
- PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2023
- Archive
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- Abstract
- Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precision on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we give a topological proof of the following fact. Let M be a holonomic algebraic D-module on the affine line, and denote by M-L its Fourier-Laplace transform. For a point a on the affine line, denote by l(a) the corresponding linear function on the dual affine line. Then the vanishing cycles of M at a are isomorphic to the graded component of degree l(a) of the Stokes filtration of M-L at infinity.