Arithmetic Hilbert modular varieties and forms for Γ₁(c,n)

2002/12/31 by Mladen Dimitrov, Jacques Tilouine
Mathematics · #math.NT #math.AG #msc:11F41 #msc:11G18 #msc:14D20 #msc:14G35

paper · pdf

published as in Geometric Aspects of Dwork Theory, (A. Adolphson, F. Baldassarri, P. Berthelot, N. Katz and F. Loeser eds.), Walter de Gruyter, Berlin 2004, 555-614 · 60 pages, in french, final version

arxiv created 2004/11/07 · arxiv updated 2009/11/30

Abstract

We recall first the analytic theory of the Hilbert modular varieties of level Γ₁(\mathfrakc,\mathfrakn) 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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