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
List Price: $54.00
Individual Member Price: $43.20
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Fermat’s Last Theorem: The ProofShare this page
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.
Table of Contents
Table of Contents
Fermat's Last Theorem: The Proof
Graduate students and research mathematicians interested in number theory and arithmetic geometry.
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