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

2014; 234 pp; Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-9849-9

Product Code: MMONO/245

Print ISBN: 978-0-8218-9849-9

Product Code: MMONO/245

List Price: $54.00

AMS Member Price: $43.20

MAA Member Price: $48.60

**Electronic ISBN: 978-1-4704-2044-4
Product Code: MMONO/245.E**

List Price: $54.00

AMS Member Price: $43.20

MAA Member Price: $48.60

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#### Supplemental Materials

# Fermat’s Last Theorem: The Proof

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*Takeshi Saito*

This is the second volume of the book on the
proof of Fermat's Last Theorem by Wiles and Taylor (the first volume
is published in the same series; see MMONO/243). Here the detail of
the proof announced in the first volume is fully exposed. The book
also includes basic materials and constructions in number theory and
arithmetic geometry that are used in the proof.

In the first
volume the modularity lifting theorem on Galois representations has
been reduced to properties of the deformation rings and the Hecke
modules. The Hecke modules and the Selmer groups used to study
deformation rings are constructed, and the required properties are
established to complete the proof.

The reader can learn basics
on the integral models of modular curves and their reductions modulo
\(p\) that lay the foundation of the construction of the Galois
representations associated with modular forms. More background
materials, including Galois cohomology, curves over integer rings, the
Néron models of their Jacobians, etc., are also explained in
the text and in the appendices.

#### Readership

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

#### Reviews & Endorsements

The book, together with the volume I, is very clear and thorough, and may be recommended to anyone interested in understanding one of the deepest results of the twentieth century in mathematics.

-- Zentralblatt fur Mathematik

#### Table of Contents

# Table of Contents

## Fermat's Last Theorem: The Proof

- Cover Cover11
- Title page iii4
- Copyright iv5
- Contents v6
- Preface ix10
- Modular curves over 𝐙 118
- Modular forms and Galois representations 6178
- Hecke modules 107124
- Selmer groups 143160
- Curves over discrete valuation rings 179196
- Finite commutative group scheme over 𝐙_{𝐩} 191208
- Jacobian of a curve and its Néron model 199216
- Bibliography 213230
- Symbol index 217234
- Subject index 221238
- Back Cover Back Cover1242