Counting Non-abelian Coverings of Algebraic Curve

Peisheng Yu

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arXiv · 2308.10473

Counting Non-abelian Coverings of Algebraic Curve

Peisheng Yu

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Abstract

In this article, we study the etale coverings of an algebraic curve $C$ with Galois group a semi-direct product $\mathbb{Z}/m\mathbb{Z} \rtimes \mathbb{Z}/n\mathbb{Z}$. Especially, for a given etale cyclic $n$-covering $D \to C$, we determine how many curves $E$ are there, satisfying $E \to D$ is an etale cyclic $m$-covering and $E \to C$ is Galois with non-abelian Galois group, under the assumption $gcd(m,n)=1$.

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Peisheng Yu. 2023-08-21. Counting Non-abelian Coverings of Algebraic Curve. https://arxiv.org/abs/2308.10473

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