Ax-Lindemann for $\mathcal{A}$_g

We prove the Ax-Lindemann theorem for the coarse moduli space ${\mathcal{A}}_g$ of principally polarized abelian varieties of dimension $g\ge 1$,andaffirmtheAndr\acute{e}-Oortconjectureunconditionallyfor$$\mathcal{A}$_{g}$for$g\le 6$.