In [14], D. Skabelund constructed a maximal curve over ${\mathbb{F}}_{q^4}$ as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstrass semigroup at any point P of the Skabelund curve. We show that its Weierstrass points are precisely the ${\mathbb{F}}_{q^4}$-rational points. Also we show that among the Weierstrass points, two types of Weierstrass semigroup occur: one for the ${\mathbb{F}}_q$-rational points, one for the remaining ${\mathbb{F}}_{q^4}$-rational points. For each of these two types its Apéry set is computed as well as a set of generators.

中文翻译：

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Skabelund最大曲线上的Weierstrass半群

在[14]中，D。Skabelund构造了一条最大曲线 ${\mathbb{F}}_{q^4}$作为铃木曲线的周期性覆盖。在本文中，我们明确确定了Skabelund曲线的任意P点处的Weierstrass半群的结构。我们证明它的Weierstrass点正好是${\mathbb{F}}_{q^4}$-理性点。我们还表明，在Weierstrass点中，出现两种类型的Weierstrass半群：一种为${\mathbb{F}}_q$-理性点，剩余的一个 ${\mathbb{F}}_{q^4}$-理性点。对于这两种类型中的每一种，都会计算其Apéry集以及一组生成器。