混合泰特动机与单位方程 II
数论
2020-07-15 v5 代数几何
摘要
在过去的约十五年里，Minhyong Kim 发展了一个框架，有效利用基本群来界定（甚至计算）双曲曲线上的整点。这是一个系列中的第三篇，其目标是在三穿孔直线的情形下实现 Kim 方法潜在的有效性。正如上一篇所设想的，我们构造了一个算法，其在停机时的输出可证明为整点集，而其停机性将依赖于一些猜想。我们的结果在有理数域上朝着实现目标迈进了一大步，同时触及了更高次数数域的话题。
引用
@article{arxiv.1510.01362,
title = {Mixed Tate motives and the unit equation II},
author = {Ishai Dan-Cohen},
journal= {arXiv preprint arXiv:1510.01362},
year = {2020}
}
备注
The "realization algorithm" of previous versions contained an error, so has been substantially reworked in section 3.7. Numerous inaccuracies in my account of the numerical approximation algorithm have been corrected in section 6. Finally, the Hasse principle in Galois cohomology of Condition 2.2.13 is now shown to follow from a conjecture due to Jannsen. To appear in Algebra and Number Theory