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arXiv · 2610.21529

Frey-Mazur theorem for semistable elliptic curves over function fields

Fateme Sajadi
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Abstract

Let $k$ be a field, let $B/k$ be a smooth projective geometrically integral curve, and put $K=k(B)$. We prove a Frey--Mazur type theorem for nonisotrivial semistable elliptic curves over $K$. More precisely, after fixing the genus of $B$ and the characteristic of $k$, a sufficiently large prime-to-characteristic torsion representation determines the $K$-isogeny class.

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Fateme Sajadi. 2026-10-15. Frey-Mazur theorem for semistable elliptic curves over function fields. https://arxiv.org/abs/2610.21529

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