Year: 2024
Type: preprint
Abstract: The original Riemann-Hilbert problem asks to find a Fuchsian ordinary differential equation with prescribed singularities and monodromy in the complex line. In the early 1980's Kashiwara solved a generalized version of the problem, valid on complex manifolds of any dimension. He presented it as a correspondence between regular holonomic D-modules and perverse sheaves. The analogous problem where one drops the regularity condition remained open for about thirty years. We solved it in the paper that received a 2024 Frontiers of Science Award. Our construction requires in particular an enhancement of the category of perverse sheaves. Here, using some examples in dimension one, we wish to convey the gist of the main ingredients used in our work. This is a written account of a talk given by the first named author at the International Congress of Basic Sciences on July 2024 in Beijing.
Source: arXiv (Cornell University)
Authors: D'Agnolo, Andrea, Kashiwara, Masaki
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402698374