Noncommutative motives, numerical equivalence, and semi-simplicity

Details Noncommutative motives, numerical equivalence, and semi-simplicity Noncommutative motives, numerical equivalence, and semi-simplicity

2011-05-15

arxiv.org/abs/1105.2950v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

In this article we further the study of the relationship between pure motives and noncommutative motives. Making use of Hochschild homology, we introduce the category NNum(k)_F of noncommutative numerical motives (over a base ring k and with coefficients in a field F). We prove that NNum(k)_F is abelian semi-simple and that Grothendieck's category Num(k)_Q of numerical motives embeds in NNum(k)_Q after being factored out by the action of the Tate object. As an application we obtain an alternative proof of Jannsen's semi-simplicity result, which uses the noncommutative world instead of a Weil cohomology.

Affiliated with

Also associated with

No associations

Rating

Noncommutative motives, numerical equivalence, and semi-simplicity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Noncommutative motives, numerical equivalence, and semi-simplicity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative motives, numerical equivalence, and semi-simplicity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-241387