Speaker: Si Ying Lee (Harvard)

Title: Modular forms on Hilbert modular varieties

Abstract:

following Sections 1.0-1.8 of

Katz, p-adic L-functions for CM fields, Invent. Math. 49 (1978), no. 3, 199-297.

Abstract: We will give an overview of Katz's paper on the construction of p-adic L-functions for CM fields. A key input in this paper is the consideration of modular forms on Hilbert modular varieties. We will discuss some key properties of Hilbert-Blumenthal abelian varieties, and the associated moduli spaces. We will also define modular forms on Hilbert modular varieties, and prove a q-expansion principle.