Effective surjectivity of Galois representations of products of elliptic curves over function fields

Alina Cojocaru; Frederick Saia

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arXiv · 2510.20910

Effective surjectivity of Galois representations of products of elliptic curves over function fields

Alina Cojocaru·Frederick Saia

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Abstract

We prove an effective surjectivity result for Galois representations of products of non-isotrivial, non-isogenous elliptic curves over certain function fields of characteristic $0$. This is by way of an isogeny degree bound in this setting, generated from bounds for elliptic curves by Griffon--Pazuki and from the function field analogue of the Frey--Mazur conjecture, by employing techniques originating in work by Serre and Masser--W{\"{u}}stholz in the number field setting.

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Alina Cojocaru, Frederick Saia. 2025-10-23. Effective surjectivity of Galois representations of products of elliptic curves over function fields. https://arxiv.org/abs/2510.20910

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