A positive density of elliptic curves is diophantine stable in certain Galois extensions
Abstract
Abstract Let p ∈ { 3 , 5 } {p\in\{3,5\}} and consider a cyclic p -extension L / ℚ {L/\mathbb{Q}} . We show that there exists an effective positive density of elliptic curves E defined over ℚ {\mathbb{Q}} , ordered by height, that is diophantine stable in L .
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Forum Mathematicum
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 19 February 2026
- Language
- EN