Introduction

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2041)

Abstract

Let F be a real quadratic field of discriminant d F and different \( {\mathfrak D} \) F , and denote by σ ε Gal(F/) the nontrivial Galois automorphism of F. Associated to F is a Hilbert modular surface M. The algebraic stack M is defined as the moduli space of abelian surfaces A equipped with an action of \( {\mathcal O} \) F , and with an \( {\mathcal O} \) F -linear principal polarization; see Chap. 3 for more details. We refer to such A as \( {\mathcal O} \) F -polarized RM abelian surfaces. The abbreviation RM stands for real multiplication, and the \( {\mathcal O} \) F in \( {\mathcal O} \) F -polarization indicates that the polarization is principal (in much of the text we allow a more general class of polarizations; see Sect. 3.1). It is known that M is regular, flat over Spec(ℤ) of relative dimension two, and smooth over Spec(ℤ[1/d F ]).

Keywords

Modulus Space Green Function Eisenstein Series Abelian Surface Intersection Multiplicity 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA
  2. 2.Department of MathematicsUniversity of Wisconsin, MadisonMadisonUSA

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