Let k be an algebraically closed field. We show using Kahn's and Sujatha's theory of birational motives that a Chow motive over k whose Chow groups are all representable (in the sense of Definition 2.1) belongs to the full and thick subcategory of motives generated by the twisted motives of curves.
Soit k un corps algébriquement clos. Nous démontrons, en nous servant de la théorie des motifs birationnels développée par Kahn et Sujatha, qu'un motif de Chow défini sur k dont les groupes de Chow sont tous représentables (au sens de la définition 2.1) appartient à la sous-catégorie pleine et épaisse des motifs engendrée par les motifs de courbes tordus.
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Charles Vial 1
@article{CRMATH_2010__348_21-22_1191_0, author = {Charles Vial}, title = {Pure motives with representable {Chow} groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {1191--1195}, publisher = {Elsevier}, volume = {348}, number = {21-22}, year = {2010}, doi = {10.1016/j.crma.2010.10.017}, language = {en}, }
Charles Vial. Pure motives with representable Chow groups. Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1191-1195. doi : 10.1016/j.crma.2010.10.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.017/
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