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Pré-Publication, Document De Travail Année : 2023

Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence

Résumé

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, slighly 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.
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hal-04483363 , version 1 (29-02-2024)

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Andreas Hohl. Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence. 2024. ⟨hal-04483363⟩
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