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Introduction to Fermat’s Last Theorem. (English) Zbl 0849.11002

In this attractively written introduction, completed in late 1993, the author recalls some of the history of Fermat’s Last Theorem, and briefly mentions basic notions about elliptic curves and modular functions relevant to the proof of Fermat’s last theorem as had recently been announced by Wiles. Useful ‘boxes’ highlight notions likely to be new to the reader; they include a brief summary of various conjectures from diophantine geometry and concerning arithmetic surfaces, as well as the modularity conjecture for elliptic curves over \(\mathbb{Q}\), imply Fermat’s Last Theorem. The article concludes with a nice elementary explanation of Ribet’s level reduction essential for connecting the theory of elliptic curves to the FLT.

MSC:

11-02 Research exposition (monographs, survey articles) pertaining to number theory
11G05 Elliptic curves over global fields
11D41 Higher degree equations; Fermat’s equation
11F11 Holomorphic modular forms of integral weight
14H52 Elliptic curves
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