2011/08/01 by Grigory Garkusha, Garkusha, Grigory, Ivan Panin +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.AT #math.KT
paper · pdf · doi:10.48550/arxiv.1108.0375
This is the final version; to appear Homology, Homotopy and Applications. arXiv admin note: text overlap with arXiv:math/0108143 by other authors
arxiv created 2012/09/11 · arxiv updated 2012/09/12
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.