The homotopy sequence of the algebraic fundamental group

TL;DR

This paper proves that the homotopy sequence of the algebraic fundamental group is exact over fields of characteristic zero, clarifying a key property in algebraic topology and algebraic geometry.

Contribution

It establishes the exactness of the homotopy sequence of the algebraic fundamental group in characteristic zero, a result not previously confirmed.

Findings

Homotopy sequence is exact in characteristic zero

Provides foundational understanding for algebraic fundamental groups

Clarifies behavior of algebraic fundamental groups in characteristic zero

Abstract

In this note, we prove that the homotopy sequence of the algebraic fundamental group is exact if the base field is of characteristic 0.