# Modular Forms and Fermat's Last Theorem

## Cornell, Gary; Silverman, Joseph H.; Stevens, Glenn

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This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

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Recensione:

"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 professionals alike, 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)

Contenuti:

I An Overview of the Proof of Fermat’s Last Theorem.- II A Survey of the Arithmetic Theory of Elliptic Curves.- III Modular Curves, Hecke Correspondences, and L-Functions.- IV Galois Coharnology.- V Finite Flat Group Schemes.- VI Three Lectures on the Modularity of % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacuaHbpGCgaqea8aadaWgaaWcbaWdbiaadweacaGGSaGaaG4maaWd % aeqaaaaa!3A7D! $${{\bar{\rho }}_{{E,3}}}$$ and the Langlands Reciprocity Conjecture.- VII Serre’s Conjectures.- VIII An Introduction to the Deformation Theory of Galois Representations.- IX Explicit Construction of Universal Deformation Rings.- X Hecke Algebras and the Gorenstein Property.- XI Criteria for Complete Intersections.- XII ?-adic Modular Deformations and Wiles’s “Main Conjecture”.- XIII The Flat Deformation Functor.- XIV Hecke Rings and Universal Deformation Rings.- XV Explicit Families of Elliptic Curves with Prescribed Mod NRepresentations.- XVI Modularity of Mod 5 Representations.- XVII An Extension of Wiles’ Results.- Appendix to Chapter XVII Classification of % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacuaHbpGCgaqea8aadaWgaaWcbaWdbiaadweacaGGSaGaeS4eHWga % paqabaaaaa!3AF1! $${{\bar{\rho }}_{{E,\ell }}}$$ by the jInvariant of E.- XVIII Class Field Theory and the First Case of Fermat’s Last Theorem.- XIX Remarks on the History of Fermat’s Last Theorem 1844 to 1984.- XX On Ternary Equations of Fermat Type and Relations with Elliptic Curves.- XXI Wiles’ Theorem and the Arithmetic of Elliptic Curves.

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## 1.Modular Forms and Fermat's Last Theorem

Editore: Springer Verlag, Secaucus, New Jersey, U.S.A. (2000)
ISBN 10: 0387989986 ISBN 13: 9780387989983
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Descrizione libro Springer Verlag, Secaucus, New Jersey, U.S.A., 2000. Soft cover. Condizione libro: Brand New. 12mo - over 6¾ - 7¾" tall. US edition Brand New SOFT COVER standard delivery. Codice libro della libreria 001029

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## 2.Modular Forms and Fermat s Last Theorem (Paperback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 0387989986 ISBN 13: 9780387989983
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Paperback. Condizione libro: New. 1st ed. 1997. 3rd printing 2000. 229 x 163 mm. Language: English . Brand New Book. This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource. Codice libro della libreria AAU9780387989983

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## 3.Modular Forms and Fermat s Last Theorem (Paperback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 0387989986 ISBN 13: 9780387989983
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Paperback. Condizione libro: New. 1st ed. 1997. 3rd printing 2000. 229 x 163 mm. Language: English . Brand New Book. This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource. Codice libro della libreria AAU9780387989983

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## 4.Modular Forms and Fermat's Last Theorem (1st ed. 1997. 3rd printing 2000)

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ISBN 10: 0387989986 ISBN 13: 9780387989983
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Descrizione libro Springer-Verlag New York Inc. Paperback. Condizione libro: new. BRAND NEW, Modular Forms and Fermat's Last Theorem (1st ed. 1997. 3rd printing 2000), Gary Cornell, Joseph H. Silverman, Glenn Stevens, This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource. Codice libro della libreria B9780387989983

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## 5.Modular Forms and Fermat's Last Theorem

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ISBN 10: 0387989986 ISBN 13: 9780387989983
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Descrizione libro Springer-Verlag New York Inc. 2000-01-01, New York, NY, 2000. paperback. Condizione libro: New. Codice libro della libreria 9780387989983

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## 6.Modular Forms and Fermat's Last Theorem

Editore: Springer (2009)
ISBN 10: 0387989986 ISBN 13: 9780387989983
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Descrizione libro Springer, 2009. Condizione libro: New. Focuses on Andrew Wiles' proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves and the works of Frey, Serre, Ribet showing that Wiles' Theorem would complete the proof of Fermat's Last Theorem. This book reflects on the history of the problem. It describes the connections of Wiles' work with other parts of mathematics. Editor(s): Cornell, Gary; Silverman, Joseph H.; Stevens, Glenn. Num Pages: 582 pages, biography. BIC Classification: PBH. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 158 x 234 x 31. Weight in Grams: 846. . 2009. 1st ed. 1997. 3rd printing 2000. Paperback. . . . . . Codice libro della libreria V9780387989983

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## 7.Modular Forms and Fermat's Last Theorem

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Descrizione libro Springer, 2000. Condizione libro: New. book. Codice libro della libreria ria9780387989983_rkm

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## 8.Modular Forms and Fermat's Last Theorem

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Descrizione libro Springer 2000-02, 2000. Condizione libro: New. This item is printed on demand. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-LSI-06917144

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## 9.Modular Forms and Fermat's Last Theorem

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ISBN 10: 0387989986 ISBN 13: 9780387989983
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## 10.Modular Forms and Fermat's Last Theorem

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Descrizione libro Springer. Condizione libro: New. Focuses on Andrew Wiles' proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves and the works of Frey, Serre, Ribet showing that Wiles' Theorem would complete the proof of Fermat's Last Theorem. This book reflects on the history of the problem. It describes the connections of Wiles' work with other parts of mathematics. Editor(s): Cornell, Gary; Silverman, Joseph H.; Stevens, Glenn. Num Pages: 582 pages, biography. BIC Classification: PBH. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 158 x 234 x 31. Weight in Grams: 846. . 2009. 1st ed. 1997. 3rd printing 2000. Paperback. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780387989983

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