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Elliptic Curves, Modular Forms, and Fermat's Last Theorem

John H. Coates and Shing-Tung Yau, editors
Publisher: 
International Press
Publication Date: 
2010
Number of Pages: 
340
Format: 
Paperback
Edition: 
2
Price: 
29.00
ISBN: 
9781571461858
Category: 
Proceedings
We do not plan to review this book.
  1. Elliptic curves and modular forms
    1. Elliptic curves
    2. Modular curves and modular forms over C
    3. Hecke operators and Hecke theory
    4. The L-function associated to a cusp form
    5. Modular curves and modular forms over Q
    6. The Hecke algebra
    7. The Shimura construction
    8. The Shimura-Taniyama conjecture
  2. Galois theory
    1. Galois representations
    2. Representations associated to elliptic curves
    3. Galois cohomology
    4. Representations of GQl
    5. The theory of Fontaine and Laffaille
    6. Deformations of representations
    7. Deformations of Galois representations
    8. Special cases
  3. Modular forms and Galois representations
    1. From modular forms to Galois representations
    2. From Galois representations to modular forms
    3. Hecke algebras
    4. Isomorphism criteria
    5. The main theorem
    6. Applications
  4. Hecke algebras
    1. Full Hecke algebras
    2. Reduced Hecke algebras
    3. Proof of theorem 3.31
    4. Proof of theorem 3.36
    5. Homological results
  5. Commutative algebra
    1. Wiles' numerical criterion
    2. Basic properties of ФA and ηA
    3. Complete intersections and the Gorenstein condition
    4. The Congruence ideal for complete intersections
    5. Isomorphism theorems
    6. A resolution lemma
    7. A criterion for
    8. complete intersections
    9. Proof of Wiles' numerical criterion
    10. A reduction to characteristic l
    11. J-structures

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