Modular Forms and Fermat's Last Theorem - by Gary Cornell & Glenn Stevens & Joseph H Silverman (Hardcover)

About the Book

Fermat's Last Theorem baffled mathematicians for over three centuries until it was solved by Andrew Wiles of Princeton in 1993. This important book begins with an overview of the complete proof, followed by chapters surveying the mathematics behind it. Readers will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem. 15 illus.

Book Synopsis

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.