Hilbert Modular Surfaces

1. Front Matter

   Pages I-IX

   PDF

2. Introduction

   • Gerard van der Geer

   Pages 1-2

3. Notations and Conventions Concerning Quadratic Number Fields

   • Gerard van der Geer

   Pages 2-3

4. Hilbert’s Modular Group

   • Gerard van der Geer

   Pages 4-27

5. Resolution of the Cusp Singularities

   • Gerard van der Geer

   Pages 28-44

6. Local Invariants

   • Gerard van der Geer

   Pages 45-57

7. Global Invariants

   • Gerard van der Geer

   Pages 58-85

8. Modular Curves on Modular Surfaces

   • Gerard van der Geer

   Pages 86-120

9. The Cohomology of Hilbert Modular Surfaces

   • Gerard van der Geer

   Pages 121-157

10. The Classification of Hilbert Modular Surfaces

    • Gerard van der Geer

    Pages 158-186

11. Examples of Hilbert Modular Surfaces

    • Gerard van der Geer

    Pages 187-204

12. Humbert Surfaces

    • Gerard van der Geer

    Pages 205-221

13. Moduli of Abelian Schemes with Real Multiplication

    • Gerard van der Geer

    Pages 222-238

14. The Tate Conjectures for Hilbert Modular Surfaces

    • Gerard van der Geer

    Pages 239-276

15. Back Matter

    Pages 277-294

    PDF

Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.

• Canon
• Compactification
• Dimension
• Division
• Divisor
• Fundamental group
• Grad
• Invariant
• Jacobi
• Volume
• algebra
• algebraic surface
• classification
• cohomology
• geometry

• Mathematisch Instituut, Universiteit van Amsterdam, Amsterdam, The Netherlands

  Gerard Geer

Policies and ethics