Embedding problems for subgroups of the fundamental group

2009/12/26 by Manish Kumar, Kumar, Manish
Mathematics · #14H30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0912.4996

openalex publication_date 2009/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π₁(C) be the fundamental group of a smooth irreducible affine curve C over an algebraically closed field of positive characteristic. It is shown that given an embedding problem for π₁(C) there exist an open index p normal subgroup of π₁(C) so that the embedding problem restricted to this group has a solution. In particular, π₁(C) is "almost ω-free".

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• Embedding problems and open subgroups
• A criterion for solving embedding problems for the etale fundamental group of curves
• Subgroup structure of fundamental groups in positive characteristic
• Normal subgroups of fundamental groups of affine curves in positive characteristic II