Información General

• Autores: Gary Cornell, Glenn Stevens, Joseph H. Silverman
• Editores: New York : Springer-Verlag, cop. 1997
• Año de publicación: 1997
• País: Estados Unidos
• Idioma: inglés
• ISBN: 0-387-94609-8
• Texto completo no disponible (Saber más ...)

Resumen

• 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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Índice

• Contributors.- Schedule of Lectures.- Introduction.- An Overview of the Proof of Fermat's Last Therem..- A Survey of the Arithmetic Theory of Elliptic Curves.- Modular Functions and Modular Curves.- Galois Cohomology.- Finite Flat Group Schemes.- Three Lectures on the Modularity of xxx and the Langlands Reciprocity Conjecture.- Serre's Conjectures.- An Introduction to the Deformation Theory of Galois Representations.- Explicit Construction of Universal Deformation Rings.- Hecke Algebras and the Gorenstein Property.- Criteria for Complete Intersections.- l-adic Modular Deformations and Wiles's "Main Conjecture".- The Flat Deformation Functor.- Hecke Rings and Universal Deformation Rings.- Explicit Families of Elliptic Curves with Prescribed Mod N Representations.- Modularity of Mod 5 Representations.- An Extension of Wiles' Results. Appendix to Chapter- Classification of xxx by the j-invariant of E.- Class Field Theory and the First Case of Fermat's Last Theorem.- Remarks on the History of Fermat's Last Theorem 1844 to 1984.- On Ternary Equations of Fermat Type and Relations With Elliptic Curves.- Wiles' Theorem and the Arithmetic of Elliptic Curves.