A Comparison Theorem For The Pro-étale Fundamental Group

Abstract

Abstract Let $X$ be a connected scheme locally of finite type over ${\mathbb{C}}$, and let $X^{\textrm{an}}$ be its associated analytic space. In this paper, we define a comparison map from the topological fundamental group of $X^{\textrm{an}}$ to the pro-étale fundamental group of $X$.