Faltings' Height of CM Cycles and Derivative of L-Functions

Topic:Faltings' Height of CM Cycles and Derivative of L-Functions
Speaker:Tong Hai Yang
Affiliation:The University of Wisconsin at Madison
Date:Thursday, November 13
Time/Room:4:30pm - 5:30pm/Fine Hall -- 214

In this talk, we first describe a systematic way to construct `automorphic Green functions' for Kudla's special divisors on a Shimura variety of orthogonal type $(n, 2)$. We then give an explicit formula for their values at a CM cycle. This formula suggests a direct relation between the Faltings' height of these CM cycles with the central derivative of some Rankin-Selberg $L$-function. As an application, we also give an `analytic proof' of the Gross-Zagier formula without computing the local intersection numbers at finite primes. This is a joint work with Jan Bruinier.