R609, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 609室)
Abelian Varieties and Related Topics
Chia-Fu Yu (Academia Sinica)
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).