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

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

2002-12-04

arxiv.org/abs/math/0212071v3

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

Mathematics

Number Theory

28 pages, in french, final version

Scientific paper

We construct local charts for the ramified cusps of the Hilbert modular variety of level $\Gamma_1(\mathfrak{c},\mathfrak{n})$. This allows us, following closely M. Rapoport and C.-L. Chai, to construct arithmetic toroidal and minimal compactifications of these modular varieties. Some applications to modular forms are given. See our joint work with J. Tilouine for other applications.

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