2004/02/13 by Nicolas Ratazzi, Ratazzi, Nicolas
Mathematics · #11G50 #14G40 #14K22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.AG #math.NT #msc:11G50 #msc:14G40 #msc:14K22
paper · pdf · doi:10.48550/arxiv.math/0402224
correction of a small LaTeX bug : the two last pages were unvoluntarily in Italics
openalex publication_date 2004/02/13 · arxiv created 2004/02/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E/K be an elliptic curve with complex multiplication and let Kab be the Abelian closure of K. We prove in this article that there exists a constant c(E/K) such that : for all point P∈ E(K)-Etors, we have h(P)≥(c(E/K))/(D)((log log 5D)/(log 2D))13, where D=[Kab(P):Kab]. This result extends to the case of elliptic curve s with complex multiplication the previous resultof Amoroso-Zannier \citeAZ on the analogous problem on the multiplicative group \mathbbGm, and generalizes to the case of extensions of degree D the result of Baker \citebaker on the lower bound of the Néron-Tate height of the points defined over an Abelian extension of an elliptic curve with complex multiplication. This result also enables us to simplify the proof of a theorem of Viada \citeviada.