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Introduction

  • Gerard van der Geer
Chapter
  • 660 Downloads
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 16)

Abstract

If K is a totally real algebraic number field then PSL(2, D K ), with D K the ring of integers of K, is called the Hubert modular group (of K). If the degree of K over ℚ is n the n embeddings K ↪ ℝ define an embedding of PSL(2, K) into PSL(2, ℝ)n. Since PSL(2, ℝ) is the holomorphic automorphism group of the complex upper half plane ℌ the Hilbert modular group PSL(2, D K ), or more generally PSL(ℒ) with ℒ ⊂ K2 a projective D K -module of rank 2, acts on ℌ n and we can form the quotient. This is quasi-projective algebraic variety with finitely many isolated singularities and it is called a Hilbert modular variety. For n = 1 (K = ℚ) one finds the classical modular group and the j-line PSL(2, ℤ)\ ℌ. This book deals with the case where the field K is a real quadratic field.

Keywords

Real Quadratic Field Fundamental Discriminant Quadratic Number Field Hilbert Modular Surface Primitive Dirichlet Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Gerard van der Geer
    • 1
  1. 1.Mathematisch InstituutUniversiteit van AmsterdamAmsterdamThe Netherlands

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