Regular singular stratified bundles and tame ramification

2012/10/18 by Kindler, Lars · 4 citations
#14E20 #14E22 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.5077

Abstract

Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_X-coherent D_X-modules) on X without relying on resolution of singularities. The main result is that the category of regular singular stratified bundles with finite monodromy is equivalent to the category of continuous representations of the tame fundamental group on finite dimensional k-vector spaces. As a corollary we obtain that a stratified bundle with finite monodromy is regular singular if and only if it is regular singular along all curves mapping to X.

Cited by

• Relative Gieseker's problem on F-divided bundles
• F-divided bundles on normal F-finite schemes
• The étale fundamental group and F-divided sheaves in characteristic p>0
• Cohomology of the stratified fundamental group of curves

Related

• Pullback of regular singular stratified bundles and restriction to\n curves
• Stratified Vector Bundles: Examples and Constructions
• The Picard Group of Simply Connected Regular Varieties and Stratified Line Bundles
• Piecewise-regular maps
• The homotopy sequence for regular singular stratified bundles