## View abstract

### Invited talk

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

## Canonical Heights on Shimura Varieties and The Andre-Oort conjecture

### Jacob Tsimerman

#### University of Toronto, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak42f9da7b99c14935bbe64e90d75f7e64').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy42f9da7b99c14935bbe64e90d75f7e64 = 'sm&#97;rt&#97;ssj&#97;c&#111;b' + '&#64;'; addy42f9da7b99c14935bbe64e90d75f7e64 = addy42f9da7b99c14935bbe64e90d75f7e64 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text42f9da7b99c14935bbe64e90d75f7e64 = 'sm&#97;rt&#97;ssj&#97;c&#111;b' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak42f9da7b99c14935bbe64e90d75f7e64').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy42f9da7b99c14935bbe64e90d75f7e64 + '\'>'+addy_text42f9da7b99c14935bbe64e90d75f7e64+'<\/a>';

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.

Joint work with Ananth Shankar(University of Wisconsin) and Jonathan Pila(Oxford University).