Modular Forms and Galois Cohomology

　　This book provides a comprehensive account of a key (andperhaps the most important) theory upon which the Taylor–Wilesproof of Fermat's last theorem is based. The book begins with anoverview of the theory of automorphic forms on linear algebraicgroups and then covers the basic theory and results on ellipticmodular forms, including a substantial simplification of theTaylor–Wiles proof by Fujiwara and Diamond. It contains a detailedexposition of the representation theory of profinite groups(including deformation theory), as well as the Euler characteristicformulas of Galois cohomology groups. The final chapter presents aproof of a non-abelian class number formula and includes severalnew results from the author. The book will be of interest tograduate students and researchers in number theory (includingalgebraic and analytic number theorists) and arithmetic algebraicgeometry.