English

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