Fermat's Last Theorem (2-Volume Set)

Takeshi Saito (Autor)

Buch | Softcover

434 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-2216-5 (ISBN)

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Presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the greatest achievements in the history of mathematics. Crucial arguments, including the so-called $3$-$5$ trick, $R=T$ theorem, are explained in depth.

This 2-volume set (Fermat's Last Theorem: Basic Tools and Fermat's Last Theorem: The Proof) presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics.

Crucial arguments, including the so-called 3-5 trick, R=T theorem, etc., are explained in depth. The proof relies on basic background materials in number theory and arithmetic geometry, such as elliptic curves, modular forms, Galois representations, deformation rings, modular curves over the integer rings, Galois cohomology, etc. The first four topics are crucial for the proof of Fermat's Last Theorem; they are also very important as tools in studying various other problems in modern algebraic number theory. In order to facilitate understanding the intricate proof, an outline of the whole argument is described in the first preliminary chapter of the first volume.

Takeshi Saito, University of Tokyo, Japan.

Contents for Fermat's Last Theorem: Basic Tools
Synopsis
Elliptic curves
Modular forms
Galois representations
The 3-5 trick
$R=T$
Commutative algebra
Deformation rings
Appendix A. Supplements to scheme theory
Bibliography
Symbol index
Subject index
Contents for Fermat's Last Theorem: The Proof
Modular curves over $/mathbf{Z}$
Modular forms and Galois representations
Hecke modules
Selmer groups
Appendix B. Curves over discrete valuation rings
Appendix C. Finite commutative group scheme over $/mathbf{Z}_p$
Appendix D. Jacobian of a curve and its Neron model
Bibliography
Symbol index
Subject index

Erscheint lt. Verlag	30.3.2015
Reihe/Serie	Translations of Mathematical Monographs
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	500 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	1-4704-2216-6 / 1470422166
ISBN-13	978-1-4704-2216-5 / 9781470422165
Zustand	Neuware