Welcome!

Abelian varieties over C are complex tori that admit an algebraic structure.  As the only proper group varieties, they are ubiquitous in both algebraic geometry and number theory.  

In this course we will build the basic theory of abelian varieties from the ground up.  The first half will be devoted to the general theory of abelian varieties over algebraically closed fields, and we will need little more than a basic knowledge of algebraic geometry at the level of Hartshorne.  In the second half we will explore some more advanced topics.