# Ag.algebraic geometry – What integer value can be the driver of an abelian variety to \$ g \$ more than \$ mathbb Q \$?

Set a positive integer $$g$$. What a positive integer $$n$$ can be the driver of a $$g$$three-dimensional abelian variety on $$mathbb Q$$ ?

For example, as there are no abelian varieties on $$mathbb Z$$, $$N$$ it is not possible $$1$$. And for elliptical curves, $$N$$ must not be less than $$11$$.