Lecture: Thursday 10am-1pm at S17-05-11
The aim of this course is to introduce the theory of Shimura varieties, and related topics. Key topics include: Abelian varieties and p-divisible groups, definition and classification of Shimura data, canonical models, integral models, zeta functions of Shimura varieties.
Students taking the course for a grade will be required to give an in-class presentation (50%) and write a short final paper (5-10 pages, 50%) on a chosen topic. Undergraduate students interested should contact me for approval to enroll.
Lecture schedule (tentative): This is a tentative schedule:
Lecture 1: (15/1): Modular curves
Lecture 2: (22/1): Hodge structures, Shimura data, adelic formulation of Shimura varieties over C
Lecture 3: (29/1): Abelian varieties
Lecture 4: (5/2): Moduli spaces of abelian varieties
Lecture 5: (12/2): Theory of canonical models
No lecture (19/2)
Recess week (26/2)
No lecture (5/3)
Lecture 6: (12/3): p-divisible groups
Lecture 7: (19/3): Integral canonical models
Lecture 8: (26/3): mod p Shimura varieties: stratifications and structures
No lecture (2/4): NUS Well-being day
Lecture 9: Honda-Tate theory, point counting on Shimura varieties
Lecture 10: Zeta functions of Shimura varieties, student presentations
Deligne: Travaux de Shimura. Séminaire Bourbaki 13 (1970-1971): 123-165.
Deligne: Varietes de Shimura: interpretation modulaire, et techniques de construction de modeles canoniques
Lan: An example-based introduction to Shimura varieties
Milne: Introduction to Shimura varieties