An Introduction to Shimura Varieties
This is the home page of the course MAST 699H/833H: An Introduction to Shimura Varieties.
Shimura varieties emerged as a fertile ground for constructing class fields and now play a crucial role in Number Theory, providing a bridge between automorphic forms and Galois representations. We will cover foundational topics such as the notions of Hermitian symmetric domains, variations of Hodge structures, Shimura data, and canonical models of Shimura varieties. Special emphasis will be put on discussing various examples. If time permits, we will discuss (some of) the following: the Eichler-Shimura isomorphism, Matsushima’s formula, and the L2- cohomology of Siegel Shimura varieties.
Class Schedule: Tuesdays 9:00-11:45 in the CICMA room (LB 938) at Concordia University.
Textbook: There is no required textbook. Milne's Introduction to Shimura varieties, Kai-Wen Lan's An example-based introduction to Shimura varieties, and Helgason's Differential Geometry, Lie Groups, and Symmetric Spaces will be the main references.
Evaluation: Assignments 75%, Oral Presentation 25%.
Notes and Assignments: Here find the lecture notes for the class (updated weekly). Check the notes for the exercises of each assignment as well. You can hand in the solutions of each assignment in the format you prefer.
Assignment 1: Exercises 1-11 in the notes, due by Feb. 6, 2023.
Assignment 2: Exercises 12-20 in the notes, due by Mar. 7, 2023.
Assignment 3: Exercises 21-32 in the notes, due by Apr. 18, 2023.