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arXiv · 2102.12653

An Errata for: Torsion subgroups of rational elliptic curves over the compositum of all $D_4$ extensions of the rational numbers

Harris B. Daniels
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Abstract

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.

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Harris B. Daniels. 2021-02-25. An Errata for: Torsion subgroups of rational elliptic curves over the compositum of all $D_4$ extensions of the rational numbers. https://arxiv.org/abs/2102.12653

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