关于有理数的所有$D_4$扩张的合成上有理椭圆曲线的挠子群的勘误表
An Errata for: Torsion subgroups of rational elliptic curves over the compositum of all $D_4$ extensions of the rational numbers
摘要：
在[2]中，作者证明了文中定义的域$\mathbb{Q}(D_4^\infty)$与$\mathbb{Q}$的所有$D_4$扩张的合成是一致的.这一主张的证据取决于对Shafarevich的一个著名结果的误读。目的是挽救文[2]的主要结果。也就是说，当基变为$\mathbb{Q}$的所有$D_4$扩张的合成时，定义在$\mathbb{Q}$上的$E$的扭结构的分类是[2]的主要结果。文[2]中的所有主要结果仍然是正确的，只是我们不再能够证明这两个域是相等的。
英文摘要：
In [2], the author claims that the fields $\mathbb{Q}(D_4^\infty)$ defined in the paper and the compositum of all $D_4$ extensions of $\mathbb{Q}$ coincide. The proof of this claim depends on a misreading of a celebrated result by Shafarevich. The purpose is to salvage the main results of [2]. That is, the classification of torsion structures of $E$ defined over $\mathbb{Q}$ when base changed to the compositum of all $D_4$ extensions of $\mathbb{Q}$ main results of [2]. All the main results in [2] are still correct except that we are no longer able to prove that these two fields are equal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
