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arXiv · 2009.08505

A consequence of the relative Bogomolov conjecture

Vesselin Dimitrov·Ziyang Gao·Philipp Habegger
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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".

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Vesselin Dimitrov, Ziyang Gao, Philipp Habegger. 2021-06-02. A consequence of the relative Bogomolov conjecture. https://arxiv.org/abs/2009.08505

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