The Andre-Oort conjecture follows from the Colmez conjecture

The Andre-Oort conjecture follows from the Colmez conjecture

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Jacob Tsimerman, University of Toronto
IAS Room S-101

The Andre-Oort conjecture says that any subvariety of a Shimura Variety with a Zariski dense set of CM points must itself be a shimura subvariety. In recent years, this has been the subject of much work. We explain how this conjecture for the moduli space of Pricnipally polarized abelian varieties of some dimension g follows from current knowledge and a conjecture of Colmez regarding the Faltings heights of CM abelian varieties- in fact, its enough to assume an averaged version of the colmez conjecture.