Abelian Varieties

What it is about

You learn the fundamental concepts and constructions of abelian varieties within algebraic geometry. In the end you will be able to derive their most important properties and apply the learned concepts to abelian varieties in a broader geometric context.

What you will be able to do

• Understanding the fundamental terms of algebraic geometry needed for abelian varieties
• Knowledge of central theorems such as the rigidity theorem, the Seesaw principle, and the Cube theorem
• Definition and examples: abelian varieties and complex tori
• Proof knowledge: Abelian varieties are commutative and projective
• Understanding of isogenies, Tate modules and dual abelian varieties

What the module consists of

• LectureExplanation of theory and illustrating with examples
• ExerciseDiscussion of problems for application and deepening of the theorems

Teaching method

• LectureIntroduction and presentation of the theory as well as examples
• ExercisesApplying and deepening the treated results through problems