A consequence of the relative Bogomolov conjecture
Résumé
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
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