Knowledge of algebra and differential geometry.
Algebraic geometry allows us to use geometric insight to understand algebraic theories such as number theory. We will introduce the prime spectrum and its structure sheaf, and study etale extensions which are analogous to covers of manifolds. This gives us a method to introduce the etale fundamental group. As an application we show that prime numbers correspond geometrically to knots and that number theoretic reciprocity laws correspond to the linking behaviour of these knots.
Course notes available via blackboard.