Content This is the second semester of a continued one-year NCTS course in 

 

2015-16 for investigating abelian varieties and related topics. We plan to 

 

discuss the following topics: Endomorphism algebras of abelian varieties 

 

(of type D), preliminaries on Shimura varieties, preliminaries on 

 

Aralekov Geometry, Hilbert modular surfaces and Hilbert modular 

 

groups, arithmetic genera and elliptic fixed points, description of certain 

 

polarized superspecial abelian varieties over Fp, derived categories and 

 

monodromy. Lectures are given in English.

 

Time Tuesdays 9:00-12:00 February 15-June 21

 

Venue Rm 609 (Astro-Math Bldg., NTU)

 

Reference [1] Endomorphism algberas: Oort (Endomorphism Algebra of 

 

AV, 1987) Shimura (Analytic families, Ann. Math. 1963).

 

[2] Hilbert modular surfaces:

 

Hirzebruch: Enseignement Math 19 (1973).

 

Van Der Geer: Hilbert modular surfaces. Springer-Verlag (1988).

 

Bruinier, Hilbert modular forms and applications. 

 

The 1-2-3 modular forms (2008). 

 

[3] Faltings and Wueztholz: Rational Points (1984).

 

[4] Papers: Deligne’s 2 papers on Shimura varieties 

 

(Sem. Bourbaki talk and Corvallis), Kottwitz (Corvallis, 1979), 

 

Cartier (Corvallis, 1979).