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BIMSA-YMSC Tsinghua Number Theory Seminar
Heights of Special Points on Quaternionic Shimura Varieties
Heights of Special Points on Quaternionic Shimura Varieties
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Roy Zhao
Time
Monday, September 23, 2024 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
Abstract
In this talk, we will present an explicit formula for the height of a special point on a quaternionic Shimura variety in terms of Faltings heights of CM abelian varieties. This improves upon Yuan and Zhang’s work on the height of points on quaternionic Shimura curves. We will also discuss applications of this formula to proving the Large Galois Orbits Conjecture, an ingredient in the Pila—Zannier strategy for proving the Andre—Oort conjecture for Shimura varieties. We then contrast this formula with the one given by Pila, Shankar, and Tsimerman.