The Cohomology of Hilbert Modular Surfaces
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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 .
KeywordsModular Form Abelian Variety Eisenstein Series Cusp Form Hodge Structure
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