  Local system cohomology groups of the complements of hyperplane arrangements
have played an important role in the theory of hypergeometric integrals, the
topology of Milnor fibers and covering spaces. One of the important theorems is
the vanishing theorem for generic $\mathbb{C}$-local systems which goes back to
Aomoto's work. Later, Cohen, Dimca, and Orlik proved a stronger version of the
vanishing theorem. In this paper, we prove a Cohen-Dimca-Orlik type theorem for
$\mathbb{Z}$-local systems.
