2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65892We recall first the analytic theory of the Hilbert modular varieties of level $Γ_1(\mathfrak{c},\mathfrak{n})$ 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.60 pages, in french, final versionNumber TheoryAlgebraic Geometry11F41; 11G18; 14D20; 14G35text