On Galois Embedding Problems Arising from 3-Torsion of Elliptic Curves
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910216537243648 |
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| author | Gálvez, José-A. Lario, Joan-C. |
| author_facet | Gálvez, José-A. Lario, Joan-C. |
| contents | We study Galois embedding problems arising from the 3-torsion of elliptic curves defined over $\mathbb{Q}$, extending the correspondence to all possible images of mod 3 Galois representations; namely, $\operatorname{GL}_2(\mathbb{F}_3),SD_{16},D_6,D_4$ and $C_2^2$. In the cyclotomic case, we show that solvability of these embedding problems is equivalent to the existence of infinitely many elliptic curves whose 3-division fields provide the corresponding solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Galois Embedding Problems Arising from 3-Torsion of Elliptic Curves Gálvez, José-A. Lario, Joan-C. Number Theory 11R32, 14Q05 We study Galois embedding problems arising from the 3-torsion of elliptic curves defined over $\mathbb{Q}$, extending the correspondence to all possible images of mod 3 Galois representations; namely, $\operatorname{GL}_2(\mathbb{F}_3),SD_{16},D_6,D_4$ and $C_2^2$. In the cyclotomic case, we show that solvability of these embedding problems is equivalent to the existence of infinitely many elliptic curves whose 3-division fields provide the corresponding solutions. |
| title | On Galois Embedding Problems Arising from 3-Torsion of Elliptic Curves |
| topic | Number Theory 11R32, 14Q05 |
| url | https://arxiv.org/abs/2605.13590 |