A Guide to the Proof of Fermat's Last Theorem from the Modularity Theorem

Question

A few years ago, a friend of mine told me that he had taken an advanced undergraduate number theory class (so something that assumed only a knowledge of algebra and mathematical maturity) which ended with a proof that the Modularity Theorem implies Fermat's Last Theorem, maybe up to citing the statements of a few other big theorems (e.g. the $\epsilon$-conjecture/Ribet's Theorem).

I'm interested in finding a reference which explains the proof from this perspective. Of course, trying to learn all the arithmetic geometry necessary to understand what Wiles actually proved would be quite the harrowing feat, but this approach seems like it could shed light on what on earth equations of the form $a^n + b^n = c^n$ have to do with whether elliptic curves over $\mathbb{Q}$ are modular. In other words, imagine a universe where the Modularity Theorem was proved as soon as it was conjectured by Taniyama and Shimura in the 50's. What would books explaining "Wiles's proof" (or "Ribet's proof" or "Serre's proof" or "Frey's proof") contain?

It's fine if a reference assumes familiarity with relatively introductory algebraic number theory and algebraic geometry (like Hartshorne and a similar level ANT book such as Frolich and Taylor), but I'd rather it didn't expect I know, say, anything about deformations of Galois representations.

Answer 1

I think what you are asking for is too much. You can look in the book suggested in the comments---in chapter 1, Stevens gives a fairly detailed overview of the steps involved in the proof. But if you don't know algebraic number theory then I don't think you will be able to understand much of it. A minimum for reading that book would be algebraic number theory at the level of Cassels and Fröhlich (plus a number of other things).

Notwithstanding that I would suggest looking at Stevens in chapter 1 and see what you think.