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Autore principale: Knyszewski, Franciszek
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2402.17636
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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.
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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