This research establishes a Galois-theoretic trichotomy in Diophantine stability, suggesting second-order terms indicate instability in genus 0 curves.
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 toward instability.
No takes yet. Share an insight, caveat, or question.
Pagano et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: