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$K$-motives of algebraic varieties
- Source :
- Homology Homotopy Appl. 14, no. 2 (2012), 211-264
- Publication Year :
- 2012
- Publisher :
- International Press of Boston, 2012.
-
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.<br />Comment: This is the final version; to appear Homology, Homotopy and Applications. arXiv admin note: text overlap with arXiv:math/0108143 by other authors
- Subjects :
- Pure mathematics
spectral category
Triangulated category
19E08
Motivic homotopy theory
01 natural sciences
010104 statistics & probability
Mathematics - Algebraic Geometry
Mathematics (miscellaneous)
FOS: Mathematics
Algebraic Topology (math.AT)
Point (geometry)
Mathematics - Algebraic Topology
0101 mathematics
Algebra over a field
Algebraic number
55U35
Algebraic Geometry (math.AG)
Mathematics
14F42
010102 general mathematics
Algebraic variety
K-Theory and Homology (math.KT)
Motivic cohomology
Algebraic K-theory
Spectral sequence
Mathematics - K-Theory and Homology
algebraic $K$-theory
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Homology Homotopy Appl. 14, no. 2 (2012), 211-264
- Accession number :
- edsair.doi.dedup.....c7690825d0313c66a50a1fb422d5d7a7