Quotients of the Siegel upper half space

Abstract: We will first talk about Riemann's theorem of polarization of complex tori and then give canonical bijections between polarized abelian varieties and Siegel upper half-spaces. If time permits, we will also define principal level structures on abelian varieties to build isomorphisms to smooth complex analytic spaces.

Reference: The end of Section 1.1, and Section 1.2 of Genestier and Ngo, Lectures on Shimura varieties.

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.