2009/12/07 by David Harbater, Harbater, David, Katherine Stevenson +1
Computer Science · Mathematics · #14G17 #14H30 #20E18 #Algebraic Geometry (math.AG) #Constraint Satisfaction and Optimization #FOS: Mathematics #Group Theory (math.GR) #Intelligent Tutoring Systems and Adaptive Learning #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.0912.1164
openalex publication_date 2009/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the properties of the fundamental group of an affine curve over an algebraically closed field of characteristic p, from the point of view of embedding problems. In characteristic zero, the fundamental group is free, but in characteristic p it is not even ω-free. In this paper we show that it is "almost ω-free," in the sense that each finite embedding problem has a proper solution when restricted to some open subgroup. We also prove that embedding problems can always be properly solved over the given curve if suitably many additional branch points are allowed, in locations that can be specified arbitrarily; this strengthens a result of the first author.