Geometric Modular Forms and Elliptic Curves

Publisher:

World Scientific

Publication Date:

2012

Number of Pages:

454

Format:

Hardcover

Edition:

2

Price:

118.00

ISBN:

9789814368643

Category:

Textbook

We do not plan to review this book.

An Algebro-Geometric Tool Box:
- Sheaves
- Schemes
- Projective Schemes
- Categories and Functors
- Applications of the Key-Lemma
- Group Schemes
- Cartier Duality
- Quotients by a Group Scheme
- Morphisms
- Cohomology of Coherent Sheaves
- Descent
- Barsotti–Tate Groups
- Formal Scheme
Elliptic Curves:
- Curves and Divisors
- Elliptic Curves
- Geometric Modular Forms of Level 1
- Elliptic Curves over ℂ
- Elliptic Curves over p–Adic Fields
- Level Structures
- L–Functions of Elliptic Curves
- Regularity
- p–Ordinary Moduli Problems
- Deformation of Elliptic Curves
Geometric Modular Forms:
- Integrality
- Vertical Control Theorem
- Action of GL(2) on Modular Forms
Jacobians and Galois Representations:
- Jacobians of Stable Curves
- Modular Galois Representations
- Fullness of Big Galois Representations
Modularity Problems:
- Induced and Extended Galois Representations
- Some Other Solutions
- Modularity of Abelian ℚ-Varieties