Finiteness of closed arithmetic hyperbolic surface bundles

For each $g\ge 2$, we show that there are finitely many cyclic commensurability classes of closed, fibered arithmetic hyperbolic $3$-manifolds with genus $g$ fiber. More generally, we show that there are only finitely many conjugacy classes of admissible surface subgroups of PSL$_2(\mathbb{C})$ whos