A consequence of the relative Bogomolov conjecture
Number Theory
2021-06-03 v3 Algebraic Geometry
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".
Keywords
Cite
@article{arxiv.2009.08505,
title = {A consequence of the relative Bogomolov conjecture},
author = {Vesselin Dimitrov and Ziyang Gao and Philipp Habegger},
journal= {arXiv preprint arXiv:2009.08505},
year = {2021}
}
Comments
To appear in JNT Special Volume Biennal Conference 2019. Some recent results updated. Comments are welcome