Descent for projective twists of modular curves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913570968567808 |
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| author | Knyszewski, Franciszek |
| author_facet | Knyszewski, Franciszek |
| contents | Let $F$ be a number field and $p\geq7$ a rational prime. We obtain a simple descent criterion characterising those projective Galois representations $\overlineρ:G_F\to\mathrm{PGL}_2(\mathbb{F}_p)$ for which the corresponding twist $X_{\overlineρ}(p)$ of the principal modular curve of level $p$ is defined over $\mathbb{Q}$. We also give a more concrete version of this result for representations which arise from elliptic curves over cyclic number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Descent for projective twists of modular curves Knyszewski, Franciszek Number Theory Let $F$ be a number field and $p\geq7$ a rational prime. We obtain a simple descent criterion characterising those projective Galois representations $\overlineρ:G_F\to\mathrm{PGL}_2(\mathbb{F}_p)$ for which the corresponding twist $X_{\overlineρ}(p)$ of the principal modular curve of level $p$ is defined over $\mathbb{Q}$. We also give a more concrete version of this result for representations which arise from elliptic curves over cyclic number fields. |
| title | Descent for projective twists of modular curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.17636 |