Fermat's Last Theorem

Basic Tools

Takeshi Saito (Autor)

Buch | Softcover

200 Seiten

2013
American Mathematical Society (Verlag)
978-0-8218-9848-2 (ISBN)

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This book, together with the companion volume, 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. The remaining topics will be treated in the second book to be published in the same series in 2014. In order to facilitate understanding the intricate proof, an outline of the whole argument is described in the first preliminary chapter, and more details are summarised in later chapters.

Takeshi Saito, University of Tokyo, Japan

Reihe/Serie	Translations of Mathematical Monographs
Verlagsort	Providence
Sprache	englisch
Gewicht	260 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	0-8218-9848-5 / 0821898485
ISBN-13	978-0-8218-9848-2 / 9780821898482
Zustand	Neuware