Program
Abelian Varieties
Student No.:60
Time:Tue & Thu 09:50-11:25, Sep.18-Nov.15
Instructor:Gerard van der Geer  [University of Amsterdam]
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-9-18
Ending Date:2018-11-15

Description:
The theory of abelian varieties takes a central place in algebraic geometry and modern number theory. Abelian varieties are projective algebraic varieties that carry a group structure, and the combination of these two aspects leads to a beautiful and very rich theory. It exends the theory of elliptic curves, 1-dimensional abelian varieties, that play an important role in number theory. The theory of abelian varieties finds applications in many parts of mathematics,like algebraic geometry, number theory and cryptography.


This course aims to give an introduction to the general theory of Abelian Varieties. Some familiarity with basic notions in Algebraic Geometry is assumed; some rudimentary knowledge of elliptic curves will be helpful.


List of topics: Abelian varieties, line bundles, group schemes, quotients by group schemes, isogenies, the dual abelian variety, the theta group, cohomology of line bundles, the endomorphism ring, Tate modules, Jacobians.


Prerequisite:
Some familiarity with basic notions in Algebraic Geometry is assumed; some rudimentary knowledge of elliptic curves will be helpful.


Reference:
References to the literature will be given at the beginning of the course.