Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve

Abstract

Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $\varphi :A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $\varphi (P)=(Q_1,\dots ,Q_m)$ with ${\text{Rank}}_{\mathbb{Z}}(⟨Q_1,\dots ,Q_m⟩)=1$. We will study a divisibility sequence related to the point $P$ and show its relation with elliptic divisibility sequences.

Minor changes