The automorphism group of the pⁿ-torsion points of an elliptic curve over a field of characteristic p ≥ 5

2024/10/15 by Im, Bo-Hae, Kim, Hansol
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.11353

Abstract

For a field K of characteristic p≥5 and the elliptic curve E_s,t: y² = x³ + sx + t defined over the function field K(s,t) of two variables s and t, we prove that for a positive integer n, the automorphism group of the normal extension K(s,t)(E_s,t[pⁿ])/K(s,t) is isomorphic to (ℤ/pⁿℤ)^×, and its inseparable degree is pⁿ.

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