3/31/2006

Stephen Kudla
IAS

Some modular generating functions for arithmetic cycles

In this talk I will give an overview of joint work with M. Rapoport and T. Yang on the construction of generating series whose coefficients are the classes of special divisors and 0-cycles on the arithmetic surfaces attached to Shimura curves. These series are the q expansions of modular forms of genus 1 and 2 respectively. I will then describe an arithmetic inner product formula and an arithmetic Siegel-Weil formula involving these forms.  If time permits at the end, I will discuss some open problems.