Let A be a CM abelian variety, say simple of dimension g, with $End(A) = O_K$, where $K$ is a CM field of degree $2g$.
Is there an upper bound for the Faltings height $h(A)$ in terms of the discriminant $d_K$ of $K$?
Let A be a CM abelian variety, say simple of dimension g, with $End(A) = O_K$, where $K$ is a CM field of degree $2g$.
Is there an upper bound for the Faltings height $h(A)$ in terms of the discriminant $d_K$ of $K$?