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

2002/12/31 by Mladen Dimitrov
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, 527-554 · 28 pages, in french, final version

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

Abstract

We construct local charts for the ramified cusps of the Hilbert modular variety of level Γ₁(\mathfrakc,\mathfrakn). 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.

Related

• Arithmetic Hilbert modular varieties and forms for Γ₁(c,n)
• Hilbert modular forms and their applications
• Overconvergent Hilbert modular forms via perfectoid modular varieties
• Rings of Hilbert modular forms, computations on Hilbert modular surfaces, and the Oda-Hamahata conjecture
• Hilbert modular forms and Galois representations