Mathematics – K-Theory and Homology
Scientific paper
2010-06-22
Moscow Math. Journal 11 #2 (2011), p.317-402
Mathematics
K-Theory and Homology
LaTeX 2e with pb-diagram.sty, 88 pages, 6+1 commutative diagrams; v.3: additions in the "conclusions" section, other small imp
Scientific paper
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.
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