Arithmetic Hilbert modular varieties and forms for $Γ_1(c,n)$

Details Arithmetic Hilbert modular varieties and forms for $Γ_1(c,n)$ Arithmetic Hilbert modular varieties and forms for $Γ_1(c,n)$

2002-12-05

arxiv.org/abs/math/0212072v3

in Geometric Aspects of Dwork Theory, (A. Adolphson, F. Baldassarri, P. Berthelot, N. Katz and F. Loeser eds.), Walter de Gruy

Mathematics

Number Theory

60 pages, in french, final version

Scientific paper

We recall first the analytic theory of the Hilbert modular varieties of level $\Gamma_1(\mathfrak{c},\mathfrak{n})$ and their compactifications. We construct arithmetic toroidal compactifications of the universal Hilbert-Blumenthal abelian variety (and of its fiber products), over the compactifications of the Hilbert modular variety constructed by the first author. We give several applications related to Hodge theory, Hilbert-Jacobi modular forms and Hilbert modular forms of half-integer weight.

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