Modular forms and Galois cohomology
著者
書誌事項
Modular forms and Galois cohomology
（Cambridge studies in advanced mathematics, 69）
Cambridge University Press, 2000
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注記
"Transferred to digital printing 2003"--T.p. verso of 2003 printing
Bibliography: p. 330-336
Includes index
内容説明・目次
内容説明
This 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.
目次
- Preface
- 1. Overview of modular forms
- 2. Representations of a group
- 3. Representations and modular forms
- 4. Galois cohomology
- 5. Modular L-values and Selmer groups
- Bibliography
- Subject index
- List of statements
- List of symbols.
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