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The Cohomology of Hilbert Modular Surfaces

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

Abstract

All interesting cohomology of Hilbert modular surfaces lies in the middle dimension, i.e. in H2. The main part of this is the cuspidal cohomology; it carries a Hodge structure and its spaces of forms of type (p, q), p + q = 2, are described by spaces of Hilbert modular forms of weight 2. The cohomology group ℍ2(X Γ ) is the cohomology generated by the cuspidal cohomology ℍ sp 2 (X Γ ) and the classes of the Chern forms w i associated to the automorphy factors (cz i + d) 2 (i = 1, 2). It can also be described as intersection homology of X Γ .

Keywords

Modular Form Abelian Variety Eisenstein Series Cusp Form Hodge Structure 
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 1988

Authors and Affiliations

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

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