Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence

Andreas Hohl
Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Complex Variables (math.CV)
2023-07-27 16:00:00
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.
PDF: Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence.pdf
Empowered by ChatGPT