论文标题
椭圆曲线和模块化的积分点
Integral Points on Elliptic Curves and Modularity
论文作者
论文摘要
在本文中，我们证明了使用Chabauty-kim方法，证明了刺穿的有理椭圆曲线的S综合点的有限性。这扩展了KIM在复杂乘法情况下的先前结果。我们方法的关键输入是使用模块化技术证明与Chabauty-Kim方法相关的某些Selmer群体消失。
In this paper we prove the finiteness of the set of S-integral points of a punctured rational elliptic curve without complex multiplication using the Chabauty-Kim method. This extends previous results of Kim in the complex multiplication case. The key input of our approach is the use of modularity techniques to prove the vanishing of certain Selmer groups involved in the Chabauty-Kim method.
