Torsion groups of elliptic curves over some infinite abelian extensions of ℚ

2020/03/17 by Tomislav Gužvić, Gužvić, Tomislav, Ivan Krijan +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.08308

openalex publication_date 2020/03/17 · openalex created_date 2020/03/23 · openalex updated_date 2026/07/28

Abstract

We determine, for an elliptic curve E/ℚ, all the possible torsion groups E(K)_tors, where K is the compositum of all ℤ_p-extensions of ℚ. Furthermore, we prove that for an elliptic curve E/ℚ it holds that E(ℚ(μ_p^∞))_tors = E(ℚ(μ_p))_tors, for all primes p ≥ 5 and E(ℚ(μ_3^∞))_tors = E(ℚ(μ_3³))_tors, E(ℚ(μ_2^∞))_tors = E(ℚ(μ_2⁴))_tors.

Citations

• The modular curves X0(65) and X0(91) and rational isogeny

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