Cohomology of the stratified fundamental group of curves

TL;DR

This paper explores the connection between stratified cohomology and the group cohomology of the stratified fundamental group of smooth projective curves over fields of positive characteristic.

Contribution

It establishes a relationship between stratified cohomology and the fundamental group's group cohomology for algebraic curves in positive characteristic.

Findings

Identifies a correspondence between stratified cohomology and fundamental group cohomology.

Provides new insights into the structure of the stratified fundamental group.

Enhances understanding of cohomological properties of algebraic curves.

Abstract

Let X be a smooth projective curve over a perfect field k of positive characteristic. This work investigates the relationship between stratified cohomology and group cohomology of the stratified fundamental group of X.