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arXiv · 0905.4711

Generalization of a going-down theorem in the category of Chow-Grothendieck motives due to N. Karpenko

Charles De Clercq
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Abstract

Let $\mathbb{M}:=(M(X),p)$ be a direct summand of the motive associated with a geometrically split, geometrically variety over a field $F$ satisfying the nilpotence principle. We show that under some conditions on an extension $E/F$, if $\mathbb{M}$ is a direct summand of another motive $M$ over an extension $E$, then $\mathbb{M}$ is a direct summand of $M$ over $F$.

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Charles De Clercq. 2009-06-11. Generalization of a going-down theorem in the category of Chow-Grothendieck motives due to N. Karpenko. https://arxiv.org/abs/0905.4711

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