On the algebraic fundamental group of smooth varieties in characteristic $p>0$

TL;DR

This paper introduces an algebraic analog of the proalgebraic completion of the topological fundamental group for smooth varieties over fields with characteristic p>0, extending fundamental group concepts to positive characteristic settings.

Contribution

It defines a new algebraic structure in characteristic p>0 that parallels the proalgebraic completion of the topological fundamental group in complex geometry.

Findings

Provides a new framework for fundamental groups in characteristic p>0

Establishes foundational properties of the algebraic fundamental group

Bridges concepts between topology and algebraic geometry in positive characteristic

Abstract

We define an analog in characteristic $p>0$ of the proalgebraic completion of the topological fundamental group of a complex manifold.