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arXiv · 2409.12144

Diophantine stability and second order terms

Carlo Pagano·Efthymios Sofos
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Abstract

We establish a Galois-theoretic trichotomy governing Diophantine stability for genus $0$ curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine stable with probability $1$. Our asymptotic formula for the second order term exhibits strong bias towards instability.

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Carlo Pagano, Efthymios Sofos. 2024-09-18. Diophantine stability and second order terms. https://arxiv.org/abs/2409.12144

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