Faltings' height of CM cycles and Derivative of $L$functions
Faltings' height of CM cycles and Derivative of $L$functions

Tonghai Yang, University of Wisconsin, Madison
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 RankinSelberg $L$function. As an application, we also give an `analytic proof' of the GrossZagier formula without computing the local intersection numbers at finite primes. This is a joint work with Jan Bruinier.