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

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

2009-05-28

arxiv.org/abs/0905.4711v2

Mathematics

Algebraic Geometry

Scientific paper

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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