Ananth Shankar: Canonical heights on Shimura varieties and the Andre-Oort conjecture (NTWS 186)
Channel: Number Theory Web Seminar
Date: 2023-10-29

Abstract: Let S be a Shimura variety. The Andre-Oort conjecture posits that the Zariski closure of special points must be a sub Shimura subvariety of S. The Andre-Oort conjecture for A_g (the moduli space of principally polarized Abelian varieties) — and therefore its sub Shimura varieties — was proved by Jacob Tsimerman. However, this conjecture was unknown for Shimura varieties without a moduli interpretation. Binyamini-Schmidt-Yafaev build on work of Binyamini to reduce the Andre-Oort conjecture to establishing height bounds on special points. I will describe joint work with Jonathan Pila and Jacob Tsimerman where we establish these height bounds, and therefore prove the Andre Oort conjecture in full generality. 

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, October 26, 2023 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, October 27, 2023 (2am AEDT, 4am NZDT)