Modular Forms and Fermat’s Last Theorem [electronic resource] /

Modular Forms and Fermat’s Last Theorem [electronic resource] /

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, 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 volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.

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Main Authors: Cornell, Gary. editor., Silverman, Joseph H. editor., Stevens, Glenn. editor., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: New York, NY : Springer New York : Imprint: Springer, 1997
Subjects:Mathematics., Algebraic geometry., Number theory., Number Theory., Algebraic Geometry.,
Online Access:http://dx.doi.org/10.1007/978-1-4612-1974-3
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id KOHA-OAI-TEST:180619
record_format koha
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Number Theory.
Algebraic Geometry.
Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Number Theory.
Algebraic Geometry.
spellingShingle Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Number Theory.
Algebraic Geometry.
Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Number Theory.
Algebraic Geometry.
Cornell, Gary. editor.
Silverman, Joseph H. editor.
Stevens, Glenn. editor.
SpringerLink (Online service)
Modular Forms and Fermat’s Last Theorem [electronic resource] /
description This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, 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 volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.
format Texto
topic_facet Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Number Theory.
Algebraic Geometry.
author Cornell, Gary. editor.
Silverman, Joseph H. editor.
Stevens, Glenn. editor.
SpringerLink (Online service)
author_facet Cornell, Gary. editor.
Silverman, Joseph H. editor.
Stevens, Glenn. editor.
SpringerLink (Online service)
author_sort Cornell, Gary. editor.
title Modular Forms and Fermat’s Last Theorem [electronic resource] /
title_short Modular Forms and Fermat’s Last Theorem [electronic resource] /
title_full Modular Forms and Fermat’s Last Theorem [electronic resource] /
title_fullStr Modular Forms and Fermat’s Last Theorem [electronic resource] /
title_full_unstemmed Modular Forms and Fermat’s Last Theorem [electronic resource] /
title_sort modular forms and fermat’s last theorem [electronic resource] /
publisher New York, NY : Springer New York : Imprint: Springer,
publishDate 1997
url http://dx.doi.org/10.1007/978-1-4612-1974-3
work_keys_str_mv AT cornellgaryeditor modularformsandfermatslasttheoremelectronicresource
AT silvermanjosephheditor modularformsandfermatslasttheoremelectronicresource
AT stevensglenneditor modularformsandfermatslasttheoremelectronicresource
AT springerlinkonlineservice modularformsandfermatslasttheoremelectronicresource
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spelling KOHA-OAI-TEST:1806192018-07-30T23:00:48ZModular Forms and Fermat’s Last Theorem [electronic resource] / Cornell, Gary. editor. Silverman, Joseph H. editor. Stevens, Glenn. editor. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,1997.engThis volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, 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 volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.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.This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, 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 volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.Mathematics.Algebraic geometry.Number theory.Mathematics.Number Theory.Algebraic Geometry.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-1974-3URN:ISBN:9781461219743

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