Fermat’s Last Theorem. (English) Zbl 0877.11035

Darmon, Henri; Diamond, Fred; Taylor, Richard

Bott, Raoul (ed.) et al., Current developments in mathematics, 1995. Lectures of a seminar, held in Boston, MA, USA, May 7-8, 1995. Cambridge, MA: International Press. 1-107 (1-154 preliminary version 1994) (1995).

From the ‘disclaimer’: “These notes were prepared in conjunction with a series of lectures on Wiles’ work given by the authors in the seminar ‘Current Developments in Mathematics’ held in Boston, May 1995. They should be taken in the spirit of an informal transcript of these talks; they are still incomplete, and may contain oversimplifications, inaccuracies, and obscurities of exposition.”
This readable paper provides a detailed version of Wiles’ proof of Fermat’s Last Theorem in a rather more digested form than the papers of Wiles and Taylor-Wiles themselves. For a little while these excellent and instructive notes (pay no attention to that disclaimer) by experts close to Wiles were the definitive discussion of and improvement on the work of A. Wiles [Ann. Math., II. Ser. 141, 443-551 (1995; Zbl 0823.11029)] and R. Taylor and A. Wiles [ibid. 553-572 (1995; Zbl 0823.11030)]. Now, several years later, one should probably recommend that readers turn to the ‘Fermat’s Last Theorem Conference’, Boston, August, 1995 edited by Gary Cornell and Joe Silverman, Springer-Verlag 1997, which provides yet more detailed lectures – largely based on or substantially contained in the present paper. Of course, readers unfamiliar with the ideas underlying Wiles’ proof, and those requiring light entertainment, should choose first to read the reviewer’s ‘Notes on Fermat’s Last Theorem’ (Wiley-Interscience, 1996), winner of the 1996 Association of American Publishers Professional/Scholarly Publishing Award for Excellence in Mathematics. But now, that disclaimer does apply.
For the entire collection see [Zbl 0833.00016].

Reviewer: A.J.van der Poorten (North Ryde)

MSC:

11G05	Elliptic curves over global fields
11D41	Higher degree equations; Fermat’s equation
14H52	Elliptic curves
11F11	Holomorphic modular forms of integral weight

Keywords:

Fermat’s last theorem

Citations:

Zbl 0823.11029; Zbl 0823.11030