Abstract
We construct cohomology groups with compact support Hci(Xar,Z(n)) for separated schemes of finite type over a finite field which generalize Lichtenbaum's Weil-etale cohomology groups for smooth and projective schemes (see [22]). In particular, if Tate's conjecture holds, and rational and numerical equivalence agree up to torsion, then the groups Hci(Xar,Z(n)) are finitely generated, form an integral model of l-adic cohomology with compact support, and admit a formula for the special values of the ζ-function of X
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