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math.NT2020
A consequence of the relative Bogomolov conjecture
Vesselin Dimitrov, Ziyang Gao, Philipp Habegger
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 co…
math.NT2020
Exponential periods and o-minimality
Johan Commelin, Philipp Habegger, Annette Huber
Let be an exponential period. We show that the real and imaginary part of are up to signs volumes of sets definable in the o-minimal structure generated by $\…
math.NT2020
Uniformity in Mordell-Lang for curves
Vesselin Dimitrov, Ziyang Gao, Philipp Habegger
Consider a smooth, geometrically irreducible, projective curve of genus defined over a number field of degree . It has at most finitely many rational points by t…