Torsion subgroups of rational elliptic curves over the compositum of all D4 extensions of the rational numbers (vol 509, pg 535, 2018)

JOURNAL OF ALGEBRA

卷:575

Correction

Daniels, Harris B.¹ 

[1] Amherst Coll, Dept Math & Stat, Amherst, MA 01002 USA

关键词: Elliptic curve;    Torsion points;    Galois theory;   

DOI  :  10.1016/j.jalgebra.2021.02.008

来源: Elsevier

【 摘 要 】

In [2], the author claims that the fields Q(D-4(infinity)) defined in the paper and the compositum of all D-4 extensions of 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 Q when base changed to the compositum of all D-4 extensions of 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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