The automorphism group of torsion points of an elliptic curve over a field of characteristic ≥ 5

2025/04/21 by Im, Bo-Hae, Kim, Hansol
#14H52 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.14859

Abstract

For a field \mathbbK of characteristic p≥5 containing \mathbbF_p^alg and the elliptic curve E_s,t: y² = x³ + sx + t defined over the function field \mathbbK(s,t) of two variables s and t, we prove that for a non-negative positive integer e and a positive integer N which is not divisible by p, the automorphism group of the normal extension \mathbbK(s,t)(E_s,t[p^e N]) over \mathbbK(s,t) is isomorphic to (ℤ/p^eℤ)^× × SL₂ (ℤ/Nℤ).

Related

• The automorphism group of the pⁿ-torsion points of an elliptic curve over a field of characteristic p ≥ 5
• Torsion of Rational Elliptic Curves over the ℤ_p-Extensions of Quadratic Fields
• Fields generated by torsion points of elliptic curves
• Torsion groups of elliptic curves over the \mathbb Z_p-extensions of \mathbb Q
• Injectivity of the specialization homomorphism of elliptic curves