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| Main Authors: | , |
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| Format: | Preprint |
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2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2002.11341 |
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| _version_ | 1866916133847695360 |
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| author | D'Agnolo, Andrea Kashiwara, Masaki |
| author_facet | D'Agnolo, Andrea Kashiwara, Masaki |
| contents | 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 $\mathcal M$ be a holonomic algebraic $\mathcal D$-module on the affine line, and denote by ${}^{\mathsf{L}}\mathcal M$ its Fourier-Laplace transform. For a point $a$ on the affine line, denote by $\ell_a$ the corresponding linear function on the dual affine line. Then, the vanishing cycles of $\mathcal M$ at $a$ are isomorphic to the graded component of degree $\ell_a$ of the Stokes filtration of ${}^{\mathsf{L}}\mathcal M$ at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_11341 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Enhanced nearby and vanishing cycles in dimension one and Fourier transform D'Agnolo, Andrea Kashiwara, Masaki Algebraic Geometry 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 $\mathcal M$ be a holonomic algebraic $\mathcal D$-module on the affine line, and denote by ${}^{\mathsf{L}}\mathcal M$ its Fourier-Laplace transform. For a point $a$ on the affine line, denote by $\ell_a$ the corresponding linear function on the dual affine line. Then, the vanishing cycles of $\mathcal M$ at $a$ are isomorphic to the graded component of degree $\ell_a$ of the Stokes filtration of ${}^{\mathsf{L}}\mathcal M$ at infinity. |
| title | Enhanced nearby and vanishing cycles in dimension one and Fourier transform |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2002.11341 |