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K-motives of algebraic varieties

Grigory Garkusha Orcid Logo, Ivan Panin

Homology, Homotopy and Applications, Volume: 14, Issue: 2, Pages: 211 - 264

Swansea University Author: Grigory Garkusha Orcid Logo

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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 K(X,Y) as well as bivariant motivic cohomology groups Hp,q(X,Y,Z) are defined and studied. We use Grayson's machiner...

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Published in: Homology, Homotopy and Applications
ISSN: 1532-0073
Published: 2012
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa13023
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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 K(X,Y) as well as bivariant motivic cohomology groups Hp,q(X,Y,Z) are defined and studied. We use Grayson's machinery to produce the Grayson motivic spectral sequence connecting bivariant K-theory to bivariant motivic cohomology. 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.
College: College of Science
Issue: 2
Start Page: 211
End Page: 264