Arithmetic Study Group: Local Borcherds Products and Heegner Divisors
28 November 2017 14:00 in CM 219
in this talk I want to introduce local Borcherds products for idefinite unitary groups U(1,m), m >1.
Local here refers to boundary components of the symmetric domain. These functions share some properties with Borcherds products, hence the name. They can be used to study the local Picard group of a boundary component of the local symmetric domain.
I will begin by saying a few words about Borcherds products, and their main properties.
Then, I will sketch the construction of the symmetric domain for a unitary group, its boundary components, their stabilizers and a compactification theory for the local symmetric domain.
After that, I will introduce Heegner divisors and, for a fixed boundary component, the local Picard group.
This will be followed by the definition of local Borcherds and I will show how their transformation behavior can be used to describe the position of Heegner divisors in the local Picard group.
As an application, one can further obtain an obstruction statement for a certain space of definite theta-series.