Mixed Artin-Tate motives with finite coefficients
Abstract
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.
Keywords
Cite
@article{arxiv.1006.4343,
title = {Mixed Artin-Tate motives with finite coefficients},
author = {Leonid Positselski},
journal= {arXiv preprint arXiv:1006.4343},
year = {2014}
}
Comments
LaTeX 2e with pb-diagram.sty, 88 pages, 6+1 commutative diagrams; v.3: additions in the "conclusions" section, other small improvements; v.4: subsection 0.14 inserted in the Introduction, corollary added in subsection 7.3, section 9 expanded; v.5: two references added, several misprints corrected -- this is intended as the final version; v.6: several misprints corrected in section 4