Modular Forms and Galois Cohomology [Hardcover]

Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.This book provides a comprehensive account of the key theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. It begins with an overview of the theory of automorphic forms on linear algebraic groups and covers the basic theory and recent results on elliptic modular forms. It includes a detailed exposition of the representation theory of profinite groups and contains several new results from the author. The book will appeal to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.This book provides a comprehensive account of the key theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. It begins with an overview of the theory of automorphic forms on linear algebraic groups and covers the basic theory and recent results on elliptic modular forms. It includes a detailed exposition of the representation theory of profinite groups and contains several new results from the author. The book will appeal to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem. Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. He offers a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula.Preface; 1. Overview of modular forl#