## Arithmetic theta series

Stephan Kudla

University of Toronto

March 8, 2018

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

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