Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence

Abstract

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.

31 pages; v2: minor corrections and improvements of the presentation, final version to appear in Portugaliae Mathematica

References in corpus (3)

• Good formal structure for meromorphic flat connections on smooth projective surfaces
• An introduction to field extensions and Galois descent for sheaves of vector spaces
• Enhanced nearby and vanishing cycles in dimension one and Fourier transform