Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Watanabe, Tatsunari, Luo, Ma
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416354567
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