Mixed Artin–Tate motives with finite coefficients

The goal of this paper is to give an explicit description of the triangulated categories of Tate and Artin–Tate motives with finite coefficients $\mathbb Z/m$ 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. Tate motives with integral coefficients are discussed in the “Conclusions” section.