Arithmetic compactifications of the Hilbert modular varieties and Hilbert modular forms for $Γ

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65891We construct local charts for the ramified cusps of the Hilbert modular variety of level $Γ_1(\mathfrak{c},\mathfrak{n})$. 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.28 pages, in french, final versionNumber TheoryAlgebraic Geometry11F41; 11G18; 14D20; 14G35Arithmetic compactifications of the Hilbert modular varieties and Hilbert modular forms for $Γ_1(c,n)$text