Geometric Modular Forms and Elliptic Curves

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  • Geometric Modular Forms and Elliptic Curves Book Detail

  • Author : Haruzo Hida
  • Release Date : 2012
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 468
  • ISBN 13 : 9814368652
  • File Size : 9,9 MB

Geometric Modular Forms and Elliptic Curves by Haruzo Hida PDF Summary

Book Description: 1. An algebro-geometric tool box. 1.1. Sheaves. 1.2. Schemes. 1.3. Projective schemes. 1.4. Categories and functors. 1.5. Applications of the key-lemma. 1.6. Group schemes. 1.7. Cartier duality. 1.8. Quotients by a group scheme. 1.9. Morphisms. 1.10. Cohomology of coherent sheaves. 1.11. Descent. 1.12. Barsotti-Tate groups. 1.13. Formal scheme -- 2. Elliptic curves. 2.1. Curves and divisors. 2.2. Elliptic curves. 2.3. Geometric modular forms of level 1. 2.4. Elliptic curves over C. 2.5. Elliptic curves over p-adic fields. 2.6. Level structures. 2.7. L-functions of elliptic curves. 2.8. Regularity. 2.9. p-ordinary moduli problems. 2.10. Deformation of elliptic curves -- 3. Geometric modular forms. 3.1. Integrality. 3.2. Vertical control theorem. 3.3. Action of GL(2) on modular forms -- 4. Jacobians and Galois representations. 4.1. Jacobians of stable curves. 4.2. Modular Galois representations. 4.3. Fullness of big Galois representations -- 5. Modularity problems. 5.1. Induced and extended Galois representations. 5.2. Some other solutions. 5.3. Modularity of Abelian Q-varieties

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Geometric Modular Forms and Elliptic Curves

Geometric Modular Forms and Elliptic Curves

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1. An algebro-geometric tool box. 1.1. Sheaves. 1.2. Schemes. 1.3. Projective schemes. 1.4. Categories and functors. 1.5. Applications of the key-lemma. 1.6. Gr

Geometric Modular Forms and Elliptic Curves

Geometric Modular Forms and Elliptic Curves

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Total View : 1574 Views
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This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The cons