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.

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Authors

Jacob Tsimerman

University of Toronto, Toronto, Ontario, Canada