Fermat's Last Theorem: Basic Tools

Couverture
American Mathematical Soc., 1 nov. 2013 - 200 pages
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 summarized in later chapters.
 

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Table des matières

Modular forms
35
Galois representations
81
13
88
26
94
40
100
52
108
The 35 trick
111
R T
119
Commutative algebra
143
65
150
Deformation rings
159
Appendix A Supplements to scheme theory
171
Bibliography
189
70
192
Symbol Index
197
Droits d'auteur

58
127

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À propos de l'auteur (2013)

Takeshi Saito, University of Tokyo, Japan

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