Modular Forms and Galois Cohomology
By (author) Haruzo Hida
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Modular Forms and Galois Cohomology by Haruzo Hida
Book DescriptionThis book provides a comprehensive account of a key (and perhaps the most important) theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. The book begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. It contains 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 and includes several new results from the author. The book will be of interest to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.
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Book DetailsISBN: 9780521072083
(228mm x 152mm x 20mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 14-Aug-2008
Country of Publication: United Kingdom
Books By Author Haruzo Hida
Geometric Modular Forms and Elliptic Curves, Hardback (December 2011)
Provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. This book includes the construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura - Taniyama conjecture.
Hilbert Modular Forms and Iwasawa Theory, Hardback (June 2006)
The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, by a leading researcher, covers both this general area and that of Iwasawa Theory, which is currently enjoying a resurgence in popularity.
Modular Forms and Galois Cohomology, Hardback (June 2000)
Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.
Elementary Theory of L-functions and Eisenstein Series, Paperback (February 1993)» View all books by Haruzo Hida
An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise.
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