English

Relative regular Riemann-Hilbert correspondence

Algebraic Geometry 2022-08-09 v4 Complex Variables

Abstract

On the product of a complex manifold XX by a complex curve SS considered as a parameter space, we show a Riemann-Hilbert correspondence between regular holonomic relative D\mathcal D-modules (resp. complexes) on the one hand and relative perverse complexes (resp. SS-C\mathbb{C}-constructible complexes) on the other hand.

Keywords

Cite

@article{arxiv.1906.09725,
  title  = {Relative regular Riemann-Hilbert correspondence},
  author = {Luisa Fiorot and Teresa Monteiro Fernandes and Claude Sabbah},
  journal= {arXiv preprint arXiv:1906.09725},
  year   = {2022}
}

Comments

22 pages. This article improves and supersedes arXiv:1811.07151. V2: 28 pages, various corrections, new Th.2, improvement of the presentation. V3: final version to appear in the Proceedings of the London Mathematical Society. V4 Version post-publication, corrects an error in the proof of Prop.3.3 of the published version, Sections 3.2-3.4 modified

R2 v1 2026-06-23T10:01:25.737Z