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

Charles de Clercq (1)

1 UPMC - Université Pierre et Marie Curie - Paris 6

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 $F$.

Mots clés: Chow groups; Chow motives; projective homogeneous varieties; nilpotence principle

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Charles de Clercq. Generalization of a going-down theorem in the category of Chow-Grothendieck motives due to N. Karpenko. 2009. ⟨hal-00389375v2⟩