Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence

Fuente: arXiv
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Main Author: Hohl, Andreas
Format: Preprint
Published: 2023
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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
id 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