Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917965297876992 |
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| author | Hohl, Andreas |
| author_facet | Hohl, Andreas |
| contents | We study some aspects of conjugation and descent in the context of the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara. First, we give a proof of the fact that Kashiwara's conjugation functor for holonomic D-modules is compatible with the enhanced De Rham functor. Afterwards, we work out some complements on Galois descent for enhanced ind-sheaves, slightly generalizing results obtained in previous joint work with Barco, Hien and Sevenheck. Finally, we show how local decompositions of an enhanced ind-sheaf into exponentials descend to lattices over smaller fields. This shows in particular that a structure of the enhanced solutions of a meromorphic connection over a subfield of the complex numbers has implications on its generalized monodromy data (in particular, the Stokes matrices), generalizing and simplifying an argument given in our previous work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_15608 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence Hohl, Andreas Algebraic Geometry Complex Variables 14F10, 32S60, 34M40 We study some aspects of conjugation and descent in the context of the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara. First, we give a proof of the fact that Kashiwara's conjugation functor for holonomic D-modules is compatible with the enhanced De Rham functor. Afterwards, we work out some complements on Galois descent for enhanced ind-sheaves, slightly generalizing results obtained in previous joint work with Barco, Hien and Sevenheck. Finally, we show how local decompositions of an enhanced ind-sheaf into exponentials descend to lattices over smaller fields. This shows in particular that a structure of the enhanced solutions of a meromorphic connection over a subfield of the complex numbers has implications on its generalized monodromy data (in particular, the Stokes matrices), generalizing and simplifying an argument given in our previous work. |
| title | Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence |
| topic | Algebraic Geometry Complex Variables 14F10, 32S60, 34M40 |
| url | https://arxiv.org/abs/2307.15608 |