eBook, PDF

Modular Forms and Fermat's Last Theorem (eBook, PDF)

Beschreibung

The book will focus on two major topics: (1) Andrew Wiles' recent proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves; and (2) the earlier works of Frey, Serre, Ribet showing that Wiles' Theorem would complete the proof of Fermat's Last Theorem. In recognition of the historical significance of Fermat's Last Theorem, parts of the book will reflect on the history of the problem, while others will speculate on the future and describe some of the connections of Wiles's work with other parts of mathematics.

Technische Details

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• Größe: 51.92MB

Barrierefreiheit

• Text-to-Speech
• E-Mail des Verlags für Barrierefreiheitsfragen: [e-mail]
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Produktdetails

• Verlag: Springer US
• Seitenzahl: 582
• Erscheinungstermin: 1. Dezember 2013
• Englisch
• ISBN-13: 9781461219743
• Artikelnr.: 44179702

Rezensionen

Das Buch ist eine hervorragende Basis, um in die moderne Arithmetik einzudringen, und zeigt zugleich in besonderer Eindringlichkeit die Schlagkraft der in den letzten Jahrzehnten entwickelten abstrakten Methoden, um konkrete diophantische Probleme wie die Fermatsche Vermutung zu lösen. DMV Jahresbericht, Bd. 103, Heft 1, 2001.

"The story of Fermat's last theorem (FLT) and its resolution is now well known. It is now common knowledge that Frey had the original idea linking the modularity of elliptic curves and FLT, that Serre refined this intuition by formulating precise conjectures, that Ribet proved a part of Serre's conjectures, which enabled him to establish that modularity of semistable elliptic curves implies FLT, and that finally Wiles proved the modularity of semistable elliptic curves.

The purpose of the book under review is to highlight and amplify these developments. As such, the book is indispensable to any student wanting to learn the finer details of the proof or any researcher wanting to extend the subject in a higher direction. Indeed, the

subject is already expanding with the recent researches of Conrad, Darmon, Diamond, Skinner and others. ...

FLT deserves a special place in the history of civilization. Because of its simplicity, it has tantalized amateurs and professionalsalike, and its remarkable fecundity has led to the development of large areas of mathematics such as, in the last century, algebraic number theory, ring theory, algebraic geometry, and in this century, the theory of elliptic curves, representation theory, Iwasawa theory, formal groups, finite flat group schemes and deformation theory of Galois representations, to mention a few. It is as if some supermind planned it all and over the centuries had been developing diverse streams of thought only to have them fuse in a spectacular synthesis to resolve FLT. No single brain can claim expertise in all of the ideas that have gone into this "marvelous proof". In this age of specialization, where "each one of us knows more and more about less and less", it is vital for us to have an overview of the masterpiece such as the one provided by this book." (M. Ram Murty, Mathematical Reviews)