  We study special values of zeta functions of singular varieties over finite
fields. We give a new formula of special values by constructing a morphism of
homology theories, which we call regulator, from higher Chow group to weight
homology. Our regulator is defined by using the notion of weight complex for
varieties over a perfect field, which was introduced by Gillet and Soule. The
main idea of the proof of our formula of special values is to use weight
spectral sequence of homology theories, whose E1 terms are homology groups for
smooth projective schemes. Also, to calculate special values, we prove that the
weight complex for any variety over a perfect field is bounded. This
boundedness result was known by Gillet and Soule in the case that the base
field admits resolution of singularities, but not in general.
