Title: Rankin-Selberg L-function and height pairing for unitary Shimura variety of type (n-1, 1).
Speaker: Tonghai Yang
Speaker Info: Wisconsin
Since the ground-breaking Gross-Zagier formula was discovered in early 1980s, a lot of important applications have been found and a lot of work has been done in trying to understand and generalizing the far-reaching formula which gives explicit connection between arithmetic and analytic sides of modular curves. In this talk, I will talk about my joint effort with Bruinier and Howard to generalize it to unitary Shimura variety of type (n-1, 1). On the analytic side is the derivative of a Rankin-Selberg L-series between a cusp form of weight n and a theta series of weight n-1. On the arithmetic side, although we hope to get Neron-Tate pairing between cohomologically trivial divisors and cohomologically trivial 0-divisors in some special cases, we are not there yet, what we have is the hieght paring between `arithmetic Kudla-Rapoport' divisors and CM 0-cycles using a good integral model of the Shimura variety.Date: Monday, October 08, 2012