Vol. 1, No. 4, 2016

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Birational motives, I: pure birational motives

Bruno Kahn and Ramdorai Sujatha

Vol. 1 (2016), No. 4, 379–440

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.

motives, birational geometry
Mathematical Subject Classification 2010
Primary: 14C15
Secondary: 14E05
Received: 24 November 2014
Revised: 30 June 2015
Accepted: 10 August 2015
Published: 11 August 2016
Bruno Kahn
Institut de Mathématiques de Jussieu-Paris Rive Gauche
4 place Jussieu
Case 247
75252 Paris Cedex 05
Ramdorai Sujatha
Mathematics Department
University of British Columbia
Vancouver BC V6T 1Z2