2009/02/28 by Bruno Kahn, R. Sujatha, Ramdorai Sujatha · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Birational geometry #Commutative Algebra and Its Applications #Equivalence (formal languages) #Equivalence relation #Functor #Projective test #Relation (database) #math.AG #msc:14C15 #msc:14E05
paper · pdf · doi:10.2140/akt.2016.1.379
published as AKT 1 (2016) 379-440 · Correction in proof of Th. 2.4.1; to appear in Annals of K-theory
arxiv created 2015/10/28 · openalex created_date 2016/06/24 · openalex publication_date 2016/08/11 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
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.