Invariance of the tame fundamental group under base change between algebraically closed fields

TL;DR

This paper proves that the tame étale fundamental group of a connected normal scheme is unchanged when base changing between algebraically closed fields, regardless of characteristic.

Contribution

It establishes the invariance of the tame étale fundamental group under base change between algebraically closed fields, extending previous understanding.

Findings

Invariance holds for all characteristics p ≥ 0.

Applicable to connected normal schemes of finite type.

Enhances understanding of fundamental group behavior under base change.

Abstract

We show that the tame \'etale fundamental group of a connected normal finite type separated scheme remains invariant upon base change between algebraically closed fields of characteristic $p \geq 0$.