Stratified bundles and étale fundamental group

On the Stratified Vector Bundles

The stratified vector bundles on a smooth variety defined over an algebraically closed field k form a neutral Tannakian category over k. We investigate the affine group–scheme corresponding to this neutral Tannakian category.

Semistable Bundles on Curves and Reducible Representations of the Fundamental Group Hélène Esnault and Claus Hertling

A.A. Bolibruch [3] and V.P. Kostov [8] showed independently that if ρ : π1(P 1 \ Σ) → GL(n,C) is an irreducible representation of the fundamental group, then there is an algebraic bundle E together with an algebraic connection ∇ : E → Ω(log Σ)⊗ E with underlying local system ρ, with the property that E ∼= ⊕1O is algebraically trivial. Equivalently, E can be taken to be the twist L ⊗ (⊕1O) of a ...

p-adic vector bundles on curves and abelian varieties and representations of the fundamental group

The Variation of the Monodromy Group in Families of Stratified Bundles in Positive Characteristic

In this article we study smooth families of stratified bundles in positive characteristic and the variation of their monodromy group. Our aim is, in particular, to strengthen the weak form of the positive equicharacteristic p-curvature conjecture stated and proved by Esnault and Langer in [9]. The main result is that if the ground field is uncountable then the strong form holds. In the case whe...

The Fundamental Category of a Stratified Space

The fundamental groupoid of a locally 0 and 1-connected space classifies covering spaces, or equivalently local systems. When the space is topologically stratified, Treumann, based on unpublished ideas of MacPherson, constructed an ‘exit category’ (in the terminology of this paper, the ‘fundamental category’) which classifies constructible sheaves, equivalently stratified etale covers. This pap...