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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.
@article{10_4007_annals_2018_187_2_2, author = {Jacob Tsimerman}, title = {The {Andr\'e-Oort} conjecture for $\mathcal {A}_g$}, journal = {Annals of mathematics}, pages = {379--390}, publisher = {mathdoc}, volume = {187}, number = {2}, year = {2018}, doi = {10.4007/annals.2018.187.2.2}, mrnumber = {3744855}, zbl = {06841543}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.2.2/} }
TY - JOUR AU - Jacob Tsimerman TI - The André-Oort conjecture for $\mathcal {A}_g$ JO - Annals of mathematics PY - 2018 SP - 379 EP - 390 VL - 187 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.2.2/ DO - 10.4007/annals.2018.187.2.2 LA - en ID - 10_4007_annals_2018_187_2_2 ER -
Jacob Tsimerman. The André-Oort conjecture for $\mathcal {A}_g$. Annals of mathematics, Tome 187 (2018) no. 2, pp. 379-390. doi: 10.4007/annals.2018.187.2.2
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