On the logarithmic Riemann-Hilbert correspondence
type: Item
instance of: scholarly article
title: On the logarithmic Riemann-Hilbert correspondence
zbMATH Open document ID: 1100.14507
author: Arthur Ogus
published in: Documenta Mathematica
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/126671
full work available at URL: ogus.dm.html
review text: Summary: We construct a classification of coherent sheaves with an integrable log connection, or, more precisely, sheaves with an integrable connection on a smooth log analytic space \(X\) over \(\mathbb C\). We do this in three contexts: sheaves and connections which are equivariant with respect to a torus action, germs of holomorphic connections, and finally, global log analytic spaces. In each case, we construct an equivalence between the relevant category and a suitable combinatorial or topological category. In the equivariant case, the objects of the target category are graded modules endowed with a group action. We then show that every germ of a holomorphic connection has a canonical equivariant model. Global connections are classified by locally constant sheaves of modules over a (varying) sheaf of graded rings on the topological space \(X_{\log}\). Each of these equivalences is compatible with tensor product and cohomology.
Mathematics Subject Classification ID: 14F40
zbMATH DE Number: 2028848
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028848