K-motives of algebraic varieties

Grigory Garkusha; Ivan Panin

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arXiv · 1108.0375

K-motives of algebraic varieties

Grigory Garkusha·Ivan Panin

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Abstract

A kind of motivic algebra of spectral categories and modules over them is developed to introduce K-motives of algebraic varieties. As an application, bivariant algebraic K-theory as well as bivariant motivic kohomology groups are defined and studied. We use Grayson's machinery to produce the Grayson motivic spectral sequence connecting bivariant K-theory to bivariant motivic kohomology. It is shown that the spectral sequence is naturally realized in the triangulated category of K-motives constructed in the paper. It is also shown that ordinary algebraic K-theory is represented by the K-motive of the point.

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BibTeX RIS

Grigory Garkusha, Ivan Panin. 2012-09-11. K-motives of algebraic varieties. https://arxiv.org/abs/1108.0375

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