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On the Griffiths group of the cubic sevenfold. (English) Zbl 0803.14022
In this paper we prove that the Griffiths group of a general cubic sevenfold is not finitely generated, even when tensored with \(\mathbb{Q}\). Using this result and a theorem of Nori, we provide examples of varieties which have some Griffiths group not finitely generated but whose corresponding intermediate Jacobian is trivial.
Reviewer: A.Albano (Torino)

MSC:
14J40 \(n\)-folds (\(n>4\))
14K30 Picard schemes, higher Jacobians
14C15 (Equivariant) Chow groups and rings; motives
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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References:
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