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arXiv · 0710.5279

Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic

Amilcar Pacheco·Pavel Zalesski·Katherine F. Stevenson
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Abstract

Let $π_1(C)$ be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic $p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic) subgroup of $π_1(C)$. Under the hypothesis that the quotient $π_1(C)/N$ admits an infinitely generated Sylow $p$-subgroup, we prove that $N$ is indeed isomorphic to a normal (resp. characteristic) subgroup of a free profinite group of countable cardinality. As a consequence, every proper open subgroup of $N$ is a free profinite group of countable cardinality.

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Amilcar Pacheco, Pavel Zalesski, Katherine F. Stevenson. 2011-07-18. Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic. https://arxiv.org/abs/0710.5279

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