论文标题
计算3属雅各比人的扭转亚组
Computing torsion subgroups of Jacobians of hyperelliptic curves of genus 3
论文作者
论文摘要
我们介绍了一种算法，以计算有理子3属的高ellip虫曲线的雅各布式的理性扭转亚组。我们将算法的岩浆实现应用于由于Sutherland而具有较低判别的曲线数据库，以及系数较小的曲线列表。在此过程中，我们发现文献中先前未描述的几种扭转结构。该算法是由于Stoll引起的属2算法的概括，我们将其扩展到满足某些条件的Abelian品种。这个想法是使用Kummer品种计算有限场上的P-Adic扭转升降机，并检查它们是否使用高度是合理的。两者都被Stoll明确地针对属3属的雅各布人。本文部分基于第二名作者的主论文。
We introduce an algorithm to compute the rational torsion subgroup of the Jacobian of a hyperelliptic curve of genus 3 over the rationals. We apply a Magma implementation of our algorithm to a database of curves with low discriminant due to Sutherland as well as a list of curves with small coefficients. In the process, we find several torsion structures not previously described in the literature. The algorithm is a generalisation of an algorithm for genus 2 due to Stoll, which we extend to abelian varieties satisfying certain conditions. The idea is to compute p-adic torsion lifts of points over finite fields using the Kummer variety and to check whether they are rational using heights. Both have been made explicit for Jacobians of hyperelliptic curves of genus 3 by Stoll. This article is partially based on the second-named author's Master thesis.
