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Fermat’s Last Theorem: The Proof

Takeshi Saito University of Tokyo, Tokyo, Japan
Available Formats:
Softcover ISBN: 978-0-8218-9849-9
Product Code: MMONO/245
234 pp
List Price: $54.00 MAA Member Price:$48.60
AMS Member Price: $43.20 Electronic ISBN: 978-1-4704-2044-4 Product Code: MMONO/245.E 234 pp List Price:$54.00
MAA Member Price: $48.60 AMS Member Price:$43.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $81.00 MAA Member Price:$72.90
AMS Member Price: $64.80 Click above image for expanded view Fermat’s Last Theorem: The Proof Takeshi Saito University of Tokyo, Tokyo, Japan Available Formats:  Softcover ISBN: 978-0-8218-9849-9 Product Code: MMONO/245 234 pp  List Price:$54.00 MAA Member Price: $48.60 AMS Member Price:$43.20
 Electronic ISBN: 978-1-4704-2044-4 Product Code: MMONO/245.E 234 pp
 List Price: $54.00 MAA Member Price:$48.60 AMS Member Price: $43.20 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:$81.00
MAA Member Price: $72.90 AMS Member Price:$64.80
• Book Details

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
Volume: 2452014
MSC: Primary 11;

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.

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

This item is also available as part of a set:

• Chapters
• Modular curves over $\mathbf {Z}$
• Modular forms and Galois representations
• Hecke modules
• Selmer groups
• Curves over discrete valuation rings
• Finite commutative group scheme over $\mathbf {Z}_p$
• Jacobian of a curve and its Néron model

• Reviews

• 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
• Request Review Copy
• Get Permissions
Iwanami Series in Modern Mathematics
Volume: 2452014
MSC: Primary 11;

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.

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

This item is also available as part of a set:
• Chapters
• Modular curves over $\mathbf {Z}$
• Modular forms and Galois representations
• Hecke modules
• Selmer groups
• Curves over discrete valuation rings
• Finite commutative group scheme over $\mathbf {Z}_p$
• Jacobian of a curve and its Néron model
• 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
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