Introduction to Shimura Varieties

The course meets every Monday, 15h15-17h in PHH333. 

COURSE DESCRIPTION 

A graduate course on Shimura varieties. The aim is to provide the basic background on Shimura varieties. Some of the topics to be discussed are: 

• Hermitian symmetric domains 
• Hodge structures 
• Shimura data, connected Shimura varieties and Shimura varieties 
• Canonical models 
• Complex multiplication and special points 
• Galois action on special points and connected components 
• Shimura varieties of PEL type 
• The zeta function of a Shimura variety 

LECTURE NOTES

• Hermitian symmetric domains
• Hodge structures and Shimura data
• Locally symmetric varieties 
• Harish-Chandra embedding 
• Connected Shimura varieties and Shimura varieties 

HOMEWORKS

These are indicated as exercises in the lecture notes and are closely related to what we cover in class, so I recommend that you look at them. 

REFERENCES

• Milne, Introduction to Shimura varieties
• Milne, Shimura varieties and moduli
• Deligne, Travaux de Shimura 
• Cornut, A course on Shimura varieties at Jussieu
• B. Conrad, A Stanford seminar on Shimura varieties
• V. Rotgers, Introductory notes for a seminar in Barcelona 
• A. Genestier and B.C.Ngo - good notes on PEL Shimura varieties
• M. Harris - A course on Shimura varieties in Jussieu 
• P. Clark - Good notes on Shimura curves