An Errata for: Torsion subgroups of rational elliptic curves over the compositum of all D₄ extensions of the rational numbers

2021/02/25 by Harris B. Daniels, Daniels, Harris B.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2102.12653

openalex publication_date 2021/02/25 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

Abstract

In [2], the author claims that the fields ℚ(D₄^∞) defined in the paper and the compositum of all D₄ 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 D₄ 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.

Related

• Torsion subgroups of rational elliptic curves over the compositum of all\n D₄ extensions of the rational numbers
• Torsion of elliptic curves with rational j-invariant over the maximal elementary abelian 2-extension of ℚ
• Torsion of Rational Elliptic Curves over the ℤ_p-Extensions of Quadratic Fields
• Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of ℚ
• Torsion groups of elliptic curves over some infinite abelian extensions of ℚ