**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2014; 434 pp; Softcover

MSC: Primary 11;

**Print ISBN: 978-1-4704-2216-5**

Product Code: MMONO/243/245

Product Code: MMONO/243/245

List Price: $91.00

AMS Member Price: $72.80

MAA Member Price: $81.90

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#### Supplemental Materials

# Fermat’s Last Theorem (2-Volume Set)

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*Takeshi Saito*

This 2-volume set (Fermat's Last Theorem: Basic
Tools and 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. In order to facilitate understanding the
intricate proof, an outline of the whole argument is described in the first
preliminary chapter of the first volume.

#### Readership

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