Minisymposium: Heights of CM Abelian Varieties

Room: Y27H28

10:00-11:00, Lucia Mocz (Princeton), Faltings' height of CM abelian varieties

Abstract: The Colmez Conjecture, a theorem in several cases due to Colmez and Obus, gives an expression of the Faltings' height of an abelian variety in terms of the logarithmic derivative of an L-function whenever the abelian variety has CM by a maximal order. In this talk, we extend this formula to larger classes of orders and derive lower bounds on the Faltings' height to provide new Northcott properties for CM abelian varieties.

11:30-12:30, Shou-Wu Zhang (Princeton), CM points and derivatives of L-functions

Abstract: I will talk about recent work of Tsimerman about reducing the Andre-Oort conjecture to an averaged version of Colmez' conjecture, and some related work on derivatives of L-functions by Zhiwei Yun and Wei Zhang using Drinfeld's moduli of Shtukas, and by Xinyi Yuan using Shimura curves.