Arithmetic Geometry and Number Theory RTG Seminar: Heights in families of abelian varieties and the Geometric Bogomolov Conjecture

Seminar | November 6 | 3:10-5 p.m. | 891 Evans Hall

 Ziyang Gao, Princeton University/CNRS

 Department of Mathematics

Given an abelian scheme over a smooth curve over a number field, we can associate two height functions: 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.

Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.