Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908510693883904 |
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| author | Barańczuk, Stefan Naskręcki, Bartosz Verzobio, Matteo |
| author_facet | Barańczuk, Stefan Naskręcki, Bartosz Verzobio, Matteo |
| contents | Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $ϕ:A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $ϕ(P)=(Q_1,\dots, Q_m)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve Barańczuk, Stefan Naskręcki, Bartosz Verzobio, Matteo Number Theory 11B39, 11G05, 11G10, 14K02 Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $ϕ:A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $ϕ(P)=(Q_1,\dots, Q_m)$ 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. |
| title | Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve |
| topic | Number Theory 11B39, 11G05, 11G10, 14K02 |
| url | https://arxiv.org/abs/2309.09699 |