2003/04/03 by Nicolas Ratazzi, Ratazzi, Nicolas
Mathematics · #11G50 #11J86 #14G40 #14K12 #14K22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G50 #msc:11J86 #msc:14G40 #msc:14K12 #msc:14K22
paper · pdf · doi:10.48550/arxiv.math/0304046
15 pages, proof of lemme 3 corrected
openalex publication_date 2003/04/03 · arxiv created 2004/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain a lower bound for the normalised height of a non-torsion subvariety V of a C.M. abelian variety. This lower bound is optimal in terms of the geometric degree of V, up to a power of a ``log''. We thus extend the results of F. Amoroso and S. David on the same problem on a multiplicative group \mathbbGmn. We prove furthermore that the optimal lower bound (conjectured by S. David and P. Philippon) is a corollary of the conjecture of S. David and M. Hindry on the abelian Lehmer's problem. We deduce these results from a density theorem on the non-torsion points of V.