Arithmetic theta series

Workshop on Representation Theory and Analysis on Locally Symmetric Spaces
Topic:Arithmetic theta series
Speaker:Stephan Kudla
Affiliation:University of Toronto
Date:Thursday, March 8
Time/Room:2:30pm - 3:30pm/Simonyi Hall 101

Abstract: In recent joint work with Jan Bruinier, Ben Howard, Michael Rapoport and Tonghai Yang, we proved that a certain generating series for the classes of arithmetic divisors on a regular integral model M of a Shimura variety for a unitary group of signature (n-1,1) for an imaginary quadratic field is a modular form of weight n valued in the first arithmetic Chow group of M. I will discuss how this is proved, highlighting the main steps. Key ingredients include information about the divisors of Borcherds forms on the integral model and the behavior of Green functions at the boundary.