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Bibliographic Details
Main Author: Knyszewski, Franciszek
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.17636
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Table of 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.