InhaltsangabeContributors.- 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.

InhaltsangabeI 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 % frxb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % 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 % frxb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % 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.