We prove that two cusps of the same dimension in the Baily–Borel compactification
of some classical series of modular varieties are linearly dependent in the
rational Chow group of the compactification. This gives a higher dimensional
analogue of the Manin–Drinfeld theorem. As a consequence, we obtain a higher
dimensional generalization of modular units as higher Chow cycles on the modular
variety.
