  We construct a cohomology theory with compact support H^i_c(X_ar,Z(n))$ for
separated schemes of finite type over a finite field, which should play a role
analog to Lichtenbaum's Weil-etale cohomology groups for smooth and projective
schemes. In particular, if Tate's conjecture holds and rational and numerical
equivalence agree up to torsion, then the groups H^i_c(X_ar,Z(n)) are finitely
generated, form an integral version of l-adic cohomology with compact support,
and admit a formula for the special values of the zeta-function of X.
