可视化椭圆曲线Shafarevich-Tate群中的四阶元素
数论
2011-03-02 v3
摘要
设E是定义在数域K上的椭圆曲线。设h是E的Shafarevich-Tate群中的一个四阶元素。我们证明h在同构意义下在无穷多个阿贝尔曲面中是可见的。也就是说，存在无穷多个阿贝尔曲面J，使得E嵌入J，并且h位于自然映射H^1(K,E)→H^1(K,J)的核中。
引用
@article{arxiv.1102.2980,
title = {Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve},
author = {Mohammad Sadek},
journal= {arXiv preprint arXiv:1102.2980},
year = {2011}
}
备注
This paper has been drawn by the author due to an error in the proof of Theorem 4.1