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Invited talk

Thursday, July 22, 14:45 ~ 15:45 UTC-3

Canonical Heights on Shimura Varieties and The Andre-Oort conjecture

Jacob Tsimerman

The Andre-Oort conjecture describes how CM points lie in algebraic subvarieties of Shimura varieties. Through a series of works by many authors, the conjecture had been reduced to establishing an upper bound on the height of CM points, which has been shown in the case of the Siegel modular variety $\mathcal{A}_g$ . We explain how to deduce this height bound in general by reducing to the case of $\mathcal{A}_g$ using a classical idea of Deligne. To carry out this idea we construct a variant of the Faltings height for arbitrary Shimura varieties, so that we may compare heights between distinct Shimura Varieties. We do this in the case of proper Shimura varieties using recent ideas in relative p-adic hodge theory.