Mazur's Growth Number Conjecture in the Rank One Case
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909579996037120 |
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| author | Kundu, Debanjana Lei, Antonio |
| author_facet | Kundu, Debanjana Lei, Antonio |
| contents | Let $p\geq 5$ be a prime number. Let $\mathsf{E}/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. Let $K$ be an imaginary quadratic field where $p$ splits, and such that the generalized Heegner hypothesis holds. Under mild hypotheses, we show that if the $p$-adic height of the Heegner point of $\mathsf{E}$ over $K$ is non-zero, then Mazur's conjecture on the growth of Selmer coranks in the $\mathbb{Z}_p^2$-extension of $K$ holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mazur's Growth Number Conjecture in the Rank One Case Kundu, Debanjana Lei, Antonio Number Theory Let $p\geq 5$ be a prime number. Let $\mathsf{E}/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. Let $K$ be an imaginary quadratic field where $p$ splits, and such that the generalized Heegner hypothesis holds. Under mild hypotheses, we show that if the $p$-adic height of the Heegner point of $\mathsf{E}$ over $K$ is non-zero, then Mazur's conjecture on the growth of Selmer coranks in the $\mathbb{Z}_p^2$-extension of $K$ holds. |
| title | Mazur's Growth Number Conjecture in the Rank One Case |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.10761 |