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 $g\ge 1$, and affirm the André-Oort conjecture unconditionally for $\mathcal{A}_{g}$ for $g\le 6$.

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