A Comparison Theorem For The Pro-\'etale Fundamental Group

TL;DR

This paper introduces a comparison map linking the topological and pro-étale fundamental groups for complex varieties, providing insights into their relationship.

Contribution

It constructs a new comparison map between topological and pro-étale fundamental groups for complex varieties, enhancing understanding of their connection.

Findings

Established a comparison map between fundamental groups

Clarified the relationship between topological and pro-étale groups

Provided new tools for studying complex varieties

Abstract

In this paper, we construct a comparison map from the topological fundamental group to the pro-\'etale fundamental group for a complex variety.