  The goal of this paper is to give an explicit description of the triangulated
categories of Tate and Artin-Tate motives with finite coefficients Z/m over a
field K containing a primitive m-root of unity as the derived categories of
exact categories of filtered modules over the absolute Galois group of K with
certain restrictions on the successive quotients. This description is
conditional upon (and its validity is equivalent to) certain Koszulity
hypotheses about the Milnor K-theory/Galois cohomology of K. This paper also
purports to explain what it means for an arbitrary nonnegatively graded ring to
be Koszul. Exact categories, silly filtrations, and the K(\pi,1)-conjecture are
discussed in the appendices. Tate motives with integral coefficients are
considered in the "Conclusions" section.
