Heights and moments of abelian varieties

In number theory and diophantine geometry, the theory of "heights" is essential in studying finiteness questions. Roughly, they capture the "arithmetic complexity" of the object of study. We give a formula relating various notions of heights of abelian varieties. We also discuss the case of Jacobians in some detail, where graphs and electrical networks will play a key role.

Based on joint works with Robin de Jong (Leiden).