Arithmetic compactifications of the Hilbert modular varieties and Hilbert modular forms for $Γ_1(c,n)$

Mladen Dimitrov

paper

Arithmetic compactifications of the Hilbert modular varieties and Hilbert modular forms for $Γ_{1} (c, n)$

arXiv:math/0212071

Abstract

We construct local charts for the ramified cusps of the Hilbert modular variety of level $Γ_{1} (c, n)$ . 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 version

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

Abstract

Arithmetic compactifications of the Hilbert modular varieties and Hilbert modular forms for $Γ_{1} (c, n)$