On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in $\mathbb{Z}_p$-extensions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918321267408896 |
|---|---|
| author | Gajek-Leonard, Rylan Hatley, Jeffrey Kundu, Debanjana Lei, Antonio |
| author_facet | Gajek-Leonard, Rylan Hatley, Jeffrey Kundu, Debanjana Lei, Antonio |
| contents | Let $p$ be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve $E/\mathbb{Q}$ over $\mathbb{Z}_p$-extensions of an imaginary quadratic field, where $p$ is a prime of good reduction for $E$. In particular, we obtain criteria that may be checked through explicit calculation, thus allowing for the verification of Mazur's conjecture in specific examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in $\mathbb{Z}_p$-extensions Gajek-Leonard, Rylan Hatley, Jeffrey Kundu, Debanjana Lei, Antonio Number Theory 11R23 Let $p$ be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve $E/\mathbb{Q}$ over $\mathbb{Z}_p$-extensions of an imaginary quadratic field, where $p$ is a prime of good reduction for $E$. In particular, we obtain criteria that may be checked through explicit calculation, thus allowing for the verification of Mazur's conjecture in specific examples. |
| title | On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in $\mathbb{Z}_p$-extensions |
| topic | Number Theory 11R23 |
| url | https://arxiv.org/abs/2401.07792 |