Fermat's last theorem : basic tools
Author(s)
Bibliographic Information
Fermat's last theorem : basic tools
（Translations of mathematical monographs, v. 243）（Iwanami series in modern mathematics）
American Mathematical Society, c2013
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フェルマー予想
Feruma yoso (Fermat conjecture)
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
"First published 2009 by Iwanami Shoten, publishers, Tokyo"--T.p. verso
Includes bibliographical references (p. 189-196) and indexes
Description and Table of Contents
Description
This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics. Crucial arguments, including the so-called $3$-$5$ trick, $R=T$ theorem, etc., are explained in depth. The proof relies on basic background materials in number theory and arithmetic geometry, such as elliptic curves, modular forms, Galois representations, deformation rings, modular curves over the integer rings, Galois cohomology, etc. The first four topics are crucial for the proof of Fermat's Last Theorem; they are also very important as tools in studying various other problems in modern algebraic number theory. The remaining topics will be treated in the second book to be published in the same series in 2014. In order to facilitate understanding the intricate proof, an outline of the whole argument is described in the first preliminary chapter, and more details are summarised in later chapters.
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