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Hilbert Modular Surfaces

  • Book
  • © 1988

Overview

Authors:
  1. Gerard Geer

    1. Mathematisch Instituut, Universiteit van Amsterdam, Amsterdam, The Netherlands

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter 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
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About this book

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.

Authors and Affiliations

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

    Gerard Geer

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