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We study special values of zeta functions of singular varieties over finitefields. We give a new formula of special values by constructing a morphism ofhomology theories, which we call regulator, from higher Chow group to weighthomology. Our regulator is defined by using the notion of weight complex forvarieties over a perfect field, which was introduced by Gillet and Soule. Themain idea of the proof of our formula of special values is to use weightspectral sequence of homology theories, whose E1 terms are homology groups forsmooth projective schemes. Also, to calculate special values, we prove that theweight complex for any variety over a perfect field is bounded. Thisboundedness result was known by Gillet and Soule in the case that the basefield admits resolution of singularities, but not in general.

Special values of zeta functions of varieties over finite fields via higher Chow groups