Descent for projective twists of modular curves

Franciszek Knyszewski

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arXiv · 2402.17636

Descent for projective twists of modular curves

Franciszek Knyszewski

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Abstract

Let $F$ be a number field and $p\geq7$ a rational prime. We obtain a simple descent criterion characterising those projective Galois representations $\overline\rho:G_F\to\mathrm{PGL}_2(\mathbb{F}_p)$ for which the corresponding twist $X_{\overline\rho}(p)$ 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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Franciszek Knyszewski. 2024-02-27. Descent for projective twists of modular curves. https://arxiv.org/abs/2402.17636

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