Hermitian symmetric domains and locally symmetric varieties

Abstract: The goal of this week's talk is to give the necessary background for the definition of a Shimura variety, to be given next week. In the first part of the talk, we will discuss hermitian symmetric domains and their groups of automorphisms (including the homomorphism from U_1 associated with each point and Cartan involutions on the associated real adjoint group). In the second part, we will define arithmetic groups and state some of the main theorems about the algebraic variety structure and group of automorphisms of the quotients of hermitian symmetric domains by torsion-free arithmetic groups.

Reference: Milne, Introduction to Shimura varieties, Chapter 1 and 3.

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.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

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.