# Heights in families of abelian varieties

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Ziyang Gao , Princeton University
Fine Hall 214

Please note location:  Fine 214.  Given an abelian scheme over a smooth curve over a number field, we can associate two height function: the fiberwise defined Neron-Tate height and a height function on the base curve. For any irreducible subvariety X of this abelian scheme, we prove that the Neron-Tate height of any point in an explicit Zariski open subset of X can be uniformly bounded from below by the height of its projection to the base curve. We use this height inequality to prove the Geometric Bogomolov Conjecture over characteristic 0. This is joint work with Philipp Habegger.