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 Andr\'e-Oort conjecture unconditionally for $\mathcal{A}_{g}$ for $g\le 6$. 
Jonathan Pila, Jacob Tsimerman
math.NT math.LO