A recommended roadmap to Fermat's Last Theorem - MathOverflow

A recommended roadmap to Fermat's Last Theorem

2012-05-24T07:22:55Z

I was inspired to undertake math as a career after watching a documentary on the proof of Fermat's Last Theorem. As such it's been a small goal of mine to understand Wiles et al's proof.

In a similar vein to this question, I was hoping to get a roadmap as to the required topics, with either suggested books or papers to read, I would be required to learn undertake this task. I am, in particular, looking for expository papers on Galois representations of elliptic curves and deformations of Galois representations.

As for my background I am currently a first year graduate student with the usual algebra, analysis, and topology prerequisites. I also have a course in algebraic number theory (up to the proof of the finiteness of class numbers), modular forms, and algebraic curves (up to Riemann-Roch) under my belt. I am also currently working through Silverman's AEC.

Thank you in advance for any advice given.

Answer by none for A recommended roadmap to Fermat's Last Theorem

2012-05-24T07:36:45Z

http://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem

mentions a book by Gary Cornell, among other resources.

Answer by Timo Keller for A recommended roadmap to Fermat's Last Theorem

2012-05-24T07:49:42Z

What about

Cornell-Silverman-Stevens, Modular Forms and Fermat's Last Theorem
Darmon-Diamond-Taylor, Fermat's Last Theorem, http://modular.math.washington.edu/edu/2011/581g/misc/Darmon-Diamond-Taylor-Fermats_Last_Theorem.pdf
Diamond-Shurman, A First Course in Modular Forms
some of Milne's course notes http://jmilne.org/math/CourseNotes/index.html
William Stein's course notes http://sage.math.washington.edu/edu/Fall2003/252/lectures/?

Answer by Steven Landsburg for A recommended roadmap to Fermat's Last Theorem

2012-05-24T12:54:35Z

The book edited by Cornell, Silverman and Stevens is terrific (though you'll of course find some articles more readable than others), but a less demanding alternative is Alf van der Poorten's Notes on Fermat's Last Theorem, which is really great fun to read, or to dip into. I see that there's a second edition due out in September, so you might or might not want to wait.

Edited to add: Here is Andrew Granville's review.