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

[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.

[发布日期] 2021-06-01

[关键词] Elliptic curve;Torsion points;Galois theory