
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Translations of Mathematical Monographs Iwanami Series in Modern Mathematics 2013; 200 pp; softcover Volume: 243 ISBN10: 0821898485 ISBN13: 9780821898482 List Price: US$49 Member Price: US$39.20 Order Code: MMONO/243 This item is also sold as part of the following set: MMONO/243/245 See also: Number Theory 1: Fermat's Dream  Kazuya Kato, Nobushige Kurokawa and Takeshi Saito Number Theory 2: Introduction to Class Field Theory  Kazuya Kato, Nobushige Kurokawa and Takeshi Saito Fermat's Last Theorem: The Proof  Takeshi Saito Elliptic Curves, Modular Forms, and Their Lfunctions  Alvaro LozanoRobledo  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 socalled \(3\)\(5\) 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. Readership Graduate students and research mathematicians interested in number theory and arithmetic geometry. Reviews "This book can serve as an introduction to the world of modularity results and will prove valuable for anyone willing to invest some work  which of course one has to do in order to understand interesting mathematics. In the opinion of the reviewer, the author found a good balance between unavoidable omissions and desirable contents of a book like this."  Zentralblatt fur Mathematik 


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