Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of ℚ

2024/06/21 by Avci, Omer
#11G05 #11R20 #14H52 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2406.15606

Abstract

Let E be an elliptic curve defined over ℚ. In this article, we classify all groups that can arise as E(ℚ(ζ_p))_tors up to isomorphism for any prime p. When p - 1 is not divisible by small integers such as 3, 4, 5, 7, or 11, we obtain a sharper classification. For any abelian number field K, the torsion subgroup E(K)_tors is a subgroup of E(ℚ^ab)_tors. Our methods provide tools to eliminate non-realized torsion structures from the list of possibilities for E(K)_tors.

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