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Fermat’s Last Theorem: Basic Tools

Takeshi Saito University of Tokyo, Tokyo, Japan
Available Formats:
Softcover ISBN: 978-0-8218-9848-2
Product Code: MMONO/243
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-1627-0 Product Code: MMONO/243.E List Price:$49.00
MAA Member Price: $44.10 AMS Member Price:$39.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view Fermat’s Last Theorem: Basic Tools Takeshi Saito University of Tokyo, Tokyo, Japan Available Formats:  Softcover ISBN: 978-0-8218-9848-2 Product Code: MMONO/243  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-1627-0 Product Code: MMONO/243.E
 List Price: $49.00 MAA Member Price:$44.10 AMS Member Price: $39.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
Volume: 2432013; 200 pp
MSC: Primary 11;

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.

Graduate students and research mathematicians interested in number theory and arithmetic geometry.

This item is also available as part of a set:

• Chapters
• Synopsis
• Elliptic curves
• Modular forms
• Galois representations
• The 3–5 trick
• $R=T$
• Commutative algebra
• Deformation rings

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 2432013; 200 pp
MSC: Primary 11;

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.

Graduate students and research mathematicians interested in number theory and arithmetic geometry.

This item is also available as part of a set:
• Chapters
• Synopsis
• Elliptic curves
• Modular forms
• Galois representations
• The 3–5 trick
• $R=T$
• Commutative algebra
• Deformation rings
• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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