Fermat’s Last Theorem: The Proof (Translations of Mathematical Monographs) by Takeshi Saito (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have very mixed feelings about this book and the other accompanying books. They lured me into believing I could simply read them and understand FLT. And indeed the book is very well written and arguably beautiful. But in reality he refers to several theorems that he does not attempt to prove, though he does give references – but he simply says they are too hard to be included.What I discovered reading this book and the accompanying ones is that what Wiles did to finish the proof of FLT was actually the easy part. The hard part had already been done by Barry Mazur and Ken Ribet. The author simply uses Mazur’s theorem without much more than a clue to how it is proven. When I looked up the proof I realized why it was omitted – it’s basically impossible for mortals to understand. Same is true for Ribet’s theorem. So I feel like I’ve been teased. I was hoping roughly 10 years would be enough to understand these books but now I see I’d need another 30 years to get through Ribet and Mazur. So what’s the point? The books should be called “Shimura Taniyama Weil – Basic Tools” not “FLT basic tools”.

⭐The epitome fo science

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