# The André-Oort conjecture for $\mathcal{A}_g$

### Abstract

We give a proof of the André-Oort conjecture for $\mathcal{A}_g$ – the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven `averaged’ version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The André-Oort conjecture then follows from previous work of Pila and the author.

## Authors

Jacob Tsimerman

Department of Mathematics, University of Toronto,Toronto, Ontario, Canada M5S 2E4