Conic bundles and Mordell--Weil ranks of elliptic surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916440665227264 |
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| author | Meira, Felipe Zingali |
| author_facet | Meira, Felipe Zingali |
| contents | Let $k$ be a number field and $\mathcal{E}$ an elliptic curve defined over the function field $k(T)$ given by an equation of the form $y^2 = a_3x^3 + a_2x^2 + a_1x + a_0$, where $a_i \in k[T]$ and $deg(a_i) \leq 2$. We explore the conic bundle structure over the $x$-line to obtain lower and upper bounds for the Mordell--Weil rank of $\mathcal{E}(k(T))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conic bundles and Mordell--Weil ranks of elliptic surfaces Meira, Felipe Zingali Number Theory Algebraic Geometry 14J27 (Primary) 11G05 (Secondary) Let $k$ be a number field and $\mathcal{E}$ an elliptic curve defined over the function field $k(T)$ given by an equation of the form $y^2 = a_3x^3 + a_2x^2 + a_1x + a_0$, where $a_i \in k[T]$ and $deg(a_i) \leq 2$. We explore the conic bundle structure over the $x$-line to obtain lower and upper bounds for the Mordell--Weil rank of $\mathcal{E}(k(T))$. |
| title | Conic bundles and Mordell--Weil ranks of elliptic surfaces |
| topic | Number Theory Algebraic Geometry 14J27 (Primary) 11G05 (Secondary) |
| url | https://arxiv.org/abs/2410.12066 |