Gauss-Manin stratification and stratified fundamental group schemes

TL;DR

This paper introduces the Gauss-Manin stratification for stratified bundles and applies it to analyze the homotopy sequence of stratified fundamental group schemes, advancing understanding of their structure in algebraic geometry.

Contribution

It develops the concept of Gauss-Manin stratification for stratified bundles and uses it to study stratified fundamental group schemes.

Findings

Established the Gauss-Manin stratification for stratified bundles.

Analyzed the homotopy sequence of stratified fundamental group schemes.

Provided new insights into the structure of stratified fundamental groups.

Abstract

We defined the Gau\ss-Manin stratification of a stratified bundle with respect to a smooth morphism and use it to study the homotopy sequence of stratified fundamental group schemes.