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  3. Modular Forms and Galois Cohomology
  • Cited by 53
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    • Publisher:
      Cambridge University Press
      Publication date:
      18 December 2009
      29 June 2000
      ISBN:
      9780511526046
      9780521770361
      9780521072083
      DOI:
      https://doi.org/10.1017/CBO9780511526046
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.678kg, 356 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.54kg, 356 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory
      Series:
      Cambridge Studies in Advanced Mathematics (69)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory
    Series:
    Cambridge Studies in Advanced Mathematics (69)
    Information

    Book description

    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.

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