|
|||||
 |
|
|
Birational motives, I:
pure birational motives
Bruno Kahn and Ramdorai Sujatha |
|
Vol. 1 (2016), No. 4, 379–440
|
Abstract |
|
We define a category of pure birational motives over a field, depending on the choice of an adequate equivalence relation on algebraic cycles. It is obtained by “killing” the Lefschetz motive in the corresponding category of effective motives. For rational equivalence, it encompasses Bloch’s decomposition of the diagonal. We study the induced Chow–Künneth decompositions in this category, and establish relationships with Rost’s cycle modules and the Albanese functor for smooth projective varieties. |
Keywords
motives, birational geometry
|
Mathematical Subject Classification 2010
Primary: 14C15
Secondary: 14E05
|
Milestones
Received: 24 November 2014
Revised: 30 June 2015
Accepted: 10 August 2015
Published: 11 August 2016
|
Authors |
| Bruno Kahn | |
| Institut de Mathématiques de
Jussieu-Paris Rive Gauche 4 place Jussieu Case 247 75252 Paris Cedex 05 France |
|
| Ramdorai Sujatha | |
| Mathematics Department University of British Columbia Vancouver BC V6T 1Z2 Canada |
|
 |
