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Softcover ISBN:  9780821898499 
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Softcover ISBN:  9780821898499 
Product Code:  MMONO/245 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 
eBook ISBN:  9781470420444 
Product Code:  MMONO/245.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
Softcover ISBN:  9780821898499 
eBook ISBN:  9781470420444 
Product Code:  MMONO/245.B 
List Price:  $101.00 $76.50 
MAA Member Price:  $90.90 $68.85 
AMS Member Price:  $80.80 $61.20 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 245; 2014; 234 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in number theory and arithmetic geometry.
This item is also available as part of a set: 
Table of Contents

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


Additional Material

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


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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.

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