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A consequence of the relative Bogomolov conjecture (2009.08505v3)
Published 17 Sep 2020 in math.NT and math.AG
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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