论文标题
提起低冈曲线以用于Tuitman的算法
Lifting low-gonal curves for use in Tuitman's algorithm
论文作者
论文摘要
考虑一个有限字段$ \ mathbb {f} _q $上平滑的投影曲线$ \叠加{c} $，配备了简单分支的莫尔氏$ \ overline {c} \ to \ mathbb {p}^1美元假设char $ \，\ mathbb {f} _q> 2 $如果$ d \ leq 4 $，和char $ \，\ mathbb {f} _q> 3 $如果$ d = 5 $。在本文中，我们描述了如何有效地计算出$ \ overline {c} $的特征为零的升力，以便可以将其作为输入Tuitman的算法来计算$ \ overline {C} / \ Mathbb {f} _Q $的Hasse-weil Zeta函数。我们的方法依赖于由于Delone-Faddeev和Bhargava引起的低等级环的参数化。
Consider a smooth projective curve $\overline{C}$ over a finite field $\mathbb{F}_q$, equipped with a simply branched morphism $\overline{C} \to \mathbb{P}^1$ of degree $d \leq 5$. Assume char$\, \mathbb{F}_q > 2$ if $d \leq 4$, and char$\, \mathbb{F}_q > 3$ if $d=5$. In this paper we describe how to efficiently compute a lift of $\overline{C}$ to characteristic zero, such that it can be fed as input to Tuitman's algorithm for computing the Hasse-Weil zeta function of $\overline{C} / \mathbb{F}_q$. Our method relies on the parametrizations of low rank rings due to Delone-Faddeev and Bhargava.
