Pure motives with representable Chow groups

Charles Vial

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arXiv · 1111.3662

Pure motives with representable Chow groups

Charles Vial

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Abstract

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 belongs to the full and thick subcategory of motives generated by the twisted motives of curves. -- Motifs purs dont les groupes de Chow sont repr\'esentables. Soit $k$ un corps alg\'ebriquement clos. Nous prouvons, en nous servant de la th\'eorie des motifs birationnels d\'evelopp\'ee par Kahn et Sujatha, qu'un motif de Chow d\'efini sur $k$ dont les groupes de Chow sont tous repr\'esentables appartient \`a la sous-cat\'egorie pleine et \'epaisse des motifs engendr\'ee par les motifs de courbes tordus.

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Charles Vial. 2011-11-15. Pure motives with representable Chow groups. https://arxiv.org/abs/1111.3662

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