Year: 2014
Type: preprint
Abstract: Let X be a smooth complex manifold. Let Sol denote the solution functor for D-modules on X. Traditionally, the fully-faithfulness of Riemann-Hilbert correspondance is proved by showing that if M_1 and M_2 are regular holonomic D_X modules, then the canonical morphism of complexes of sheaves RH_{M_1,M_2} : RHom(M_1,M_2) ---> RHom(Sol(M_2),Sol(M_1)) is an isomorphism, in a derived sense. This paper has to do with the converse statement. We prove that if M is an holonomic D_X module for which RH_{M,M} is an isomorphism, then M is regular.
Source: arXiv (Cornell University)
Author: Teyssier, Jean-Baptiste
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3083633062