EVENT DETAILS AND ABSTRACT

Title: Chowla-Selberg formula and a conjecture of Colmez
Speaker: Tonghai Yang
Speaker Info: Univ. of Wisconsin, Madison
Brief Description:
Special Note:
Abstract:

In his seminal work on Mordell conjecture, Faltings introduces and studies the height of an Abelian variety. When the Abelianvvariety is a CM elliptic curve, its Falting's height is essentially the local derivative of the Dirichlet $L$-series associated to the imaginary quadratic field by the famous Chowla-Selberg formula. In 1990s, Colmez gave a precise conjectural formula to compute the Faltings height of a CM abelian variety of CM type $(E,\Phi)$ in terms of the log derivative of some `Artin' L-function associated to the CM type $\Phi$. He proved the conjecture when the CM number field when $E$ is abelian, refining Gross and Anderson's work on periods. In this talk, we will discuss a new way to attack this problem and give positive answer to a family of non-abelian CM fields. This is part of an ongoing joint work with Bruinier, Howard, Kudla, and Rapoport.