Abstract
The Neron-Tate height on an abelian variety is known to be constructed from any Weil height by a dynamical process. Similarly, we wish to obtain (dynamically) the Faltings height on a moduli space of abelian varieties by iterating a Hecke correspondence. In this direction, we study the convergence of metrics under this iteration. As an application, we give formulas on the average height of isogenous QM abelian surfaces.
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