A consequence of the relative Bogomolov conjecture

authored by

Vesselin Dimitrov, Ziyang Gao, Philipp Habegger

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".

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Cambridge
University of Basel

Type

Article

Journal

Journal of Number Theory

Volume

230

Pages

146-160

No. of pages

15

ISSN

0022-314X

Publication date

01.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.1016/j.jnt.2021.03.028 (Access: Closed)