Journal article 1140 views
K-motives of algebraic varieties
,
Ivan Panin
Homology, Homotopy and Applications, Volume: 14, Issue: 2, Pages: 211 - 264
Swansea University Author:
Grigory Garkusha
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DOI (Published version): 10.4310/HHA.2012.v14.n2.a13
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...
| Published in: | Homology, Homotopy and Applications |
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| ISSN: | 1532-0073 |
| Published: |
2012
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| Online Access: |
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| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
211 |
| End Page: |
264 |