A consequence of the relative Bogomolov conjecture

2020/09/17 by Dimitrov, Vesselin, Gao, Ziyang, Habegger, Philipp
#11G30 #11G50 #14G05 #14G25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2009.08505

Abstract

We propose a formulation of the relative Bogomolov conjecture and show that it gives an affirmative answer to a question of Mazur's concerning the uniformity of the Mordell-Lang conjecture for curves. In particular we show that the relative Bogomolov conjecture implies the uniform Manin-Mumford conjecture for curves. The proof is built up on our previous work "Uniformity in Mordell-Lang for curves".

Related

• Recent developments of the Uniform Mordell-Lang Conjecture
• The Relative Bogomolov Conjecture for Fibered Products of Elliptic Curves
• Equidistribution in Families of Abelian Varieties and Uniformity
• An Explicit Uniform Mordell Conjecture over Function Fields of Characteristic Zero
• The Uniform Mordell-Lang Conjecture