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The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes.
Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections, and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications.
Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.
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Subjects
Fermat's last theorem, Congresses, Elliptic Curves, Modular FormsEdition | Availability |
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1
Modular Forms and Fermat's Last Theorem
2013, Springer London, Limited
in English
1461219744 9781461219743
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Book Details
Edition Notes
Includes bibliographical references and index.
Papers from a conference held Aug. 9-18, 1995, at Boston University.
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