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arXiv · 1006.4343

Mixed Artin-Tate motives with finite coefficients

Leonid Positselski
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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(π,1)-conjecture are discussed in the appendices. Tate motives with integral coefficients are considered in the "Conclusions" section.

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BibTeXRIS

Leonid Positselski. 2014-04-25. Mixed Artin-Tate motives with finite coefficients. https://arxiv.org/abs/1006.4343

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