Moduli space of abelian varieties II

Abstract: Sections 2.4.-2.6 of Genestier and Ngo, Lectures on Shimura varieties. We will finish the proof that the functor $\mathcal{A}$ is represented by a smooth quasiprojective scheme. In particular, to show the smoothness of $\mathcal{A}$, we review Grothendieck and Messing's theorem on deformations of abelian schemes. Finally, if we have time, we will give an adelic description of $\mathcal{A}$ and define Hecke operators.

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 2026 topic: Explicit class field theory.

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.