• Benjamin Howard
  • Tonghai Yang
Part of the Lecture Notes in Mathematics book series (LNM, volume 2041)


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 ]).


Modulus Space Green Function Eisenstein Series Abelian Surface Intersection Multiplicity 
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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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