Fermat's Last Theorem: The Proof

Couverture
American Mathematical Soc., 18 déc. 2014 - 234 pages

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   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.

 

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Table des matières

principal actors in this proof are deformation rings and Hecke alge
3
Modular forms
7
Modular forms and Galois representations
61
Galois representations
78
Hecke modules
107
The 35 trick
111
xvii
124
Commutative algebra
143
44
171
52
177
Appendix B Curves over discrete valuation rings
179
Finite commutative group scheme over
191
Jacobian of a curve and its Néron model
199
Bibliography
213
55
214
xv
215

Deformation rings
159
35
162

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À propos de l'auteur (2014)

Takeshi Saito, University of Tokyo, Japan.

Informations bibliographiques