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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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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...

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Published in: Homology, Homotopy and Applications
ISSN: 1532-0073
Published: 2012
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URI: https://cronfa.swan.ac.uk/Record/cronfa13023
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spelling 2015-06-24T11:20:42.5258751 v2 13023 2012-10-09 K-motives of algebraic varieties 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2012-10-09 SMA 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. Journal Article Homology, Homotopy and Applications 14 2 211 264 1532-0073 29 11 2012 2012-11-29 10.4310/HHA.2012.v14.n2.a13 http://www.intlpress.com/HHA/v14/n2/a13/ COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2015-06-24T11:20:42.5258751 2012-10-09T12:55:12.3093965 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Grigory Garkusha 0000-0001-9836-0714 1 Ivan Panin 2
title K-motives of algebraic varieties
spellingShingle K-motives of algebraic varieties
Grigory Garkusha
title_short K-motives of algebraic varieties
title_full K-motives of algebraic varieties
title_fullStr K-motives of algebraic varieties
title_full_unstemmed K-motives of algebraic varieties
title_sort K-motives of algebraic varieties
author_id_str_mv 7d3826fb9a28467bec426b8ffa3a60e0
author_id_fullname_str_mv 7d3826fb9a28467bec426b8ffa3a60e0_***_Grigory Garkusha
author Grigory Garkusha
author2 Grigory Garkusha
Ivan Panin
format Journal article
container_title Homology, Homotopy and Applications
container_volume 14
container_issue 2
container_start_page 211
publishDate 2012
institution Swansea University
issn 1532-0073
doi_str_mv 10.4310/HHA.2012.v14.n2.a13
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://www.intlpress.com/HHA/v14/n2/a13/
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description 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.
published_date 2012-11-29T03:14:55Z
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