The proof of Fermat's Last Theorem by R. Taylor and A. Wiles

written by Gerd Faltings
translated from German by Uwe F. Mayer

Abstract: The proof of the conjecture mentioned in the title was finally completed in September of 1994. A. Wiles announced this result in the summer of 1993; however, there was a gap in his work. The paper of Taylor and Wiles does not close this gap but circumvents it. This article is an adaptation of several talks that I [Gerd Faltings] have given on this topic and is by no means about my own work. I have tried to present the basic ideas to a wider mathematical audience, and in the process I have skipped over certain details, which are in my opinion not so much of interest to the non-specialist. The specialists can then alleviate their boredom by finding those mistakes and correcting them.

Key words: Fermat's Last Theorem, elliptic curves, modular forms, deformations.

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