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arXiv · 2304.02778

Automorphism groups of curves over arbitrary fields

Daniel Bragg
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Abstract

We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also give a positive solution to the weak inverse Galois problem for function fields over an arbitrary field. Finally, we reduce the inverse Galois problem for function fields over an arbitrary field $K$ to the case of $K(T)$.

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Daniel Bragg. 2023-04-05. Automorphism groups of curves over arbitrary fields. https://arxiv.org/abs/2304.02778

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