2019/11/20 by Jorge Mello, Min Sha, Mello, Jorge +1
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1911.08752
18 pages
openalex publication_date 2019/11/20 · arxiv created 2022/03/27 · arxiv updated 2022/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, for an elliptic curve E defined over the algebraic numbers and for any subfield F of algebraic numbers, we say that E has the Northcott property over F if there are at most finitely many F-rational points on E of uniformly bounded height, and we say that E has the property (P) over F if for any infinite subset S of F-rational points on E, f(S) = S for an F-endomorphism f of E implies that f is an automorphism. We establish some criteria for both properties and provide typical examples. We also show that the Northcott property implies the property (P).