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arXiv · 1712.05763

Differential operators and hyperelliptic curves over finite fields

Iván Blanco-Chacón·Alberto F. Boix·Stiofáin Fordham·Emrah Sercan Yilmaz
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Abstract

Boix, De Stefani and Vanzo have characterized ordinary/supersingular elliptic curves over $\mathbb{F}_p$ in terms of the level of the defining cubic homogenous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve $\mathcal{C}$ of genus $g\geq 2$ has level $2$. We provide a good number of examples and raise a conjecture.

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Iván Blanco-Chacón, Alberto F. Boix, Stiofáin Fordham, Emrah Sercan Yilmaz. 2018-01-15. Differential operators and hyperelliptic curves over finite fields. https://doi.org/10.1016/j.ffa.2018.02.007

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