Mordell-Weil group as Galois modules
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908521453322240 |
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| author | Vavasour, Thomas Wuthrich, Christian |
| author_facet | Vavasour, Thomas Wuthrich, Christian |
| contents | We study the action of the Galois group $G$ of a finite extension $K/k$ of number fields on the points on an elliptic curve $E$. For an odd prime $p$, we aim to determine the structure of the $p$-adic completion of the Mordell-Weil group $E(K)$ as a $\mathbb{Z}_p[G]$-module only using information of $E$ over $k$ and the completions of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13365 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mordell-Weil group as Galois modules Vavasour, Thomas Wuthrich, Christian Number Theory 11G05, 11G07, 20C10 We study the action of the Galois group $G$ of a finite extension $K/k$ of number fields on the points on an elliptic curve $E$. For an odd prime $p$, we aim to determine the structure of the $p$-adic completion of the Mordell-Weil group $E(K)$ as a $\mathbb{Z}_p[G]$-module only using information of $E$ over $k$ and the completions of $K$. |
| title | Mordell-Weil group as Galois modules |
| topic | Number Theory 11G05, 11G07, 20C10 |
| url | https://arxiv.org/abs/2306.13365 |