  Beginning with the conjecture of Artin and Tate in 1966, there has been a
series of successively more general conjectures expressing the special values
of the zeta function of an algebraic variety over a finite field in terms of
other invariants of the variety. In this article, we present the ultimate such
conjecture, and provide evidence for it. In particular, we enhance Voevodsky's
Z[1/p]-category of etale motivic complexes with a p-integral structure, and
show that, for this category, our conjecture follows from the Tate and
Beilinson conjectures. As the conjecture is stated in terms of motivic
complexes, it (potentially) applies also to algebraic stacks, log varieties,
simplicial varieties, etc..
