Further examples of non-geometric sections of arithmetic fundamental groups

2021/09/30 by Mohamed Saı̈di, Mohamed Saidi, Saidi, Mohamed
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2109.14882

Accepted for publication in Publications of the Research Institute for Mathematical Sciences. arXiv admin note: text overlap with arXiv:1510.06864

arxiv created 2021/09/30 · openalex publication_date 2021/09/30 · arxiv updated 2021/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the existence of group-theoretic sections of certain geometrically pro-nilpotent by abelian arithmetic fundamental groups of hyperbolic curves over p-adic local fields which are non-geometric, i.e., which do not arise from rational points. Among these quotients is the geometrically metabelian arithmetic fundamental group.

Citations

• On the existence of non-geometric sections of arithmetic fundamental groups

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