Enhanced specialization and microlocalization

D'Agnolo, Andrea; Kashiwara, Masaki

doi:10.1007/s00029-020-00613-2

Sel. Math. New Ser.

2021

DOI: 10.1007/s00029-020-00613-2

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Enhanced specialization and microlocalization

Andrea D'Agnolo

Masaki Kashiwara

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Enhanced nearby and vanishing cycles in dimension one and Fourier transform

D'Agnolo¹,

Kashiwara²

2020

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Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precisions 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 L M 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 L M at infinity. Contents 1. Introduction 1 2. Review on enhanced ind-sheaves 6 3. Enhanced perverse ind-sheaves on a curve 9 4. Nearby and vanishing cycles 13 5. Fourier transform on the affine line 14 Appendix A. Vanishing cycles by blow-up transform 17 References 24

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Enhanced nearby and vanishing cycles in dimension one and Fourier transform

D'Agnolo¹,

Kashiwara²

2020

Preprint

View full text Add to dashboard Cite

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Enhanced specialization and microlocalization

Cited by 1 publication

References 10 publications

Enhanced nearby and vanishing cycles in dimension one and Fourier transform

Enhanced nearby and vanishing cycles in dimension one and Fourier transform

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