Arithmetic Hilbert modular varieties and forms for $Γ_1(c,n)$
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We 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 version
60 pages, in french, final version