English

Relative Regular Riemann-Hilbert correspondence II

Algebraic Geometry 2024-02-13 v6 Complex Variables

Abstract

We develop the theory of relative regular holonomic D-modules with a smooth complex manifold S of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting the relative Riemann-Hilbert correspondence proved in a previous work in the one-dimensional case.

Keywords

Cite

@article{arxiv.2203.05444,
  title  = {Relative Regular Riemann-Hilbert correspondence II},
  author = {Luisa Fiorot and Teresa Monteiro Fernandes and Claude Sabbah},
  journal= {arXiv preprint arXiv:2203.05444},
  year   = {2024}
}

Comments

V2: 58 pages, revised version following referee's comments; the arXiv version contains a last section with details. V3: Statement of Propositions 5.4(1) and A.3 corrected. V4: 61 pages Statement and proof of Proposition 5.4 corrected after a referee's remark; details of proofs added in the appendix. V5: 54 pages Final published version in the Compositio style. V6: = V5 plus details of proofs of V4

R2 v1 2026-06-24T10:08:49.809Z