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arXiv · 1608.04338

On generalizations of Fermat curves over finite fields and their automorphisms

Nazar Arakelian·Pietro Speziali
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Abstract

Let $\mathcal{X}$ be an irreducible algebraic curve defined over a finite field $\mathbb{F}_q$ of characteristic $p>2$. Assume that the $\mathbb{F}_q$-automorphism group of $\mathcal{X}$ admits as an automorphism group the direct product of two cyclic groups $C_m$ and $C_n$ of orders $m$ and $n$ prime to $p$ such that both quotient curves $\mathcal{X}/C_n$ and $\mathcal{X}/C_m$ are rational. In this paper, we provide a complete classification of such curves, as well as a characterization of their full automorphism groups.

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Nazar Arakelian, Pietro Speziali. 2016-08-15. On generalizations of Fermat curves over finite fields and their automorphisms. https://arxiv.org/abs/1608.04338

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