On the S-fundamental group scheme

TL;DR

This paper introduces a new fundamental group scheme for varieties over algebraically closed fields of positive characteristic, extending some of Simpson's results and establishing Lefschetz theorems.

Contribution

It defines a novel fundamental group scheme in positive characteristic and explores its properties and applications, generalizing prior complex-analytic results.

Findings

Introduces a new fundamental group scheme for positive characteristic varieties

Proves Lefschetz type theorems for the new group scheme

Extends results of C. Simpson to positive characteristic settings

Abstract

We introduce a new fundamental group scheme for varieties defined over an algebraically closed field of positive characteristic and we use it to study generalization of some of C. Simpson's results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.