Wiles Proof of Fermat's Last Theorem

[fibonacci235]

Just a quick question. What areas of mathematics would I have to study to understand Wiles' proof? I know his proof involves the Modularity Theorem, Elliptic Curves etc, but to really understand the proof what other topics would I need to master?

[micromass]

You need to know algebraic and arithmetic geometry quite well. Complex Analysis is probably also used.

Here are some nice books to get you started:
- Invitation to the mathematics of Fermat-Wiles by Hellegouarch
- Rational points on elliptic curves by Silverman and Tate
- Lectures on Curves, Surfaces and Projective Varieties by Beltrametti