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

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arxiv 2309.09699 v2 pith:5LRYROMY submitted 2023-09-18 math.NT

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

Stefan Bara\'nczuk , Bartosz Naskr\k{e}cki , Matteo Verzobio This is my paper
classification math.NT
keywords divisibilityellipticabeliancurvedefineddotsrelatedsequences
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $\phi:A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $\phi(P)=(Q_1,\dots, Q_m)$ with $\text{Rank}_\mathbb{Z}(\langle Q_1,\dots, Q_m\rangle)=1$. We will study a divisibility sequence related to the point $P$ and show its relation with elliptic divisibility sequences.

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  1. Remarks on a theorem of Silverman

    math.NT 2026-07 accept novelty 5.5

    Silverman-type exact reduction orders hold for elliptic curves over global function fields (n coprime to p) and for abelian-scheme sections over C when the Betti map is generically submersive.