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arXiv · 2406.12561

A positive density of elliptic curves are diophantine stable in certain Galois extensions

Anwesh Ray·Pratiksha Shingavekar
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Abstract

Let $p \in \{3, 5\}$ and consider a cyclic $p$-extension $L/\mathbb{Q}$. We show that there exists an effective positive density of elliptic curves $ E $ defined over $ \mathbb{Q} $, ordered by height, that are diophantine stable in $ L $.

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Anwesh Ray, Pratiksha Shingavekar. 2024-06-18. A positive density of elliptic curves are diophantine stable in certain Galois extensions. https://doi.org/10.1515/forum-2025-0160

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