### Mixed Artin-Tate motives with finite coefficients, by Leonid Positselski

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-th 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.

Leonid Positselski <posic@mccme.ru, positselski@yandex.ru>