论文标题
chabauty-coleman计算等级1 PICARD曲线
Chabauty-Coleman computations on rank 1 Picard curves
论文作者
论文摘要
我们可以使用chabauty-coleman方法在1403 PICARD曲线上计算1403 PICARD曲线的完整合理点。为了进行此计算，我们将Balakrishnan和Tuitman的Magma代码扩展到Coleman Integration。新代码在曲线上计算$ p $ -Adic（Coleman）积分，以在数字字段中定义的点完全分裂，并为Jacobians具有无限订单点的曲线实现有效的Chabauty，而这些曲线不是Abel-Jacobi Map下的理性点图像。我们讨论了几个有趣的曲线示例，其中chabauty-coleman集包含在数字字段上定义的点。
We provably compute the full set of rational points on 1403 Picard curves defined over $\mathbb{Q}$ with Jacobians of Mordell-Weil rank $1$ using the Chabauty-Coleman method. To carry out this computation, we extend Magma code of Balakrishnan and Tuitman for Coleman integration. The new code computes $p$-adic (Coleman) integrals on curves to points defined over number fields where the prime $p$ splits completely and implements effective Chabauty for curves whose Jacobians have infinite order points that are not the image of a rational point under the Abel-Jacobi map. We discuss several interesting examples of curves where the Chabauty-Coleman set contains points defined over number fields.
