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

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 $L$.

Version 2: 23 pages, accepted for publication in Forum Mathematicum

References in corpus (2)

• Rank growth of elliptic curves over $N$-th root extensions
• Rank stability of elliptic curves in certain non-abelian extensions