Modular forms on Hilbert modular varieties

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.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.