  We prove that all points of a toroidal compactification lying over
0-dimensional cusps are rationally equivalent in the integral Chow group of the
toroidal compactification for Siegel modular varieties, Hilbert modular
varieties and orthogonal modular varieties. This gives a generalization, and
even strengthening, of the Manin-Drinfeld theorem in higher dimension from the
viewpoint of algebraic cycles.
