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Bibliographic Details
Main Authors:	Watanabe, Tatsunari, Luo, Ma
Format:	Preprint
Published:	2025
Subjects:	Algebraic Geometry Algebraic Topology
Online Access:	https://arxiv.org/abs/2511.12354
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Table of Contents:

Over any field of characteristic $0$, we prove that the homotopy exact sequence of algebraic fundamental groups for the universal curve with unordered marked points does not split. The same nonsplitting holds for the universal hyperelliptic curve. Our approach extends Chen's topological result to the profinite setting and relies on the use of relative and continuous relative completions to detect the nonexistence of algebraic sections.