The homotopy sequence for regular singular stratified bundles

TL;DR

This paper extends the homotopy exact sequence concept to fundamental group schemes of regular singular stratified bundles, under certain compactification conditions, generalizing previous étale fundamental group results.

Contribution

It proves the existence of a homotopy exact sequence for fundamental group schemes of regular singular stratified bundles, generalizing dos Santos' work to a broader context.

Findings

Established a homotopy exact sequence for regular singular stratified bundles

Extended the theory to cases with partial compactification to log smooth morphisms

Generalized the classical étale fundamental group sequence to stratified bundles

Abstract

A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an analogous homotopy exact sequence for fundamental group schemes classifying regular singular stratified bundles, under the additional assumption that the morphism in question can be (partially) compactified to a log smooth morphism.