On complete intersections in varieties with finite-dimensional motive

R. Laterveer (Corresponding author), J. Nagel, C.A.M. Peters

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Let X be a complete intersection inside a variety M with finite-dimensional motive and for which the Lefschetz-type conjecture B(M) holds. We show how conditions on the niveau filtration on the homology of X influence directly the niveau on the level of Chow groups. This leads to a generalization of Voisin's result. The latter states that if M has trivial Chow groups and if X has non-trivial variable cohomology parametrized by c-dimensional algebraic cycles, then the cycle class maps A k (X) → H 2k (X) are injective for k<c. We give variants involving group actions, which lead to several new examples with finite-dimensional Chow motives.

Originele taal-2Engels
Pagina's (van-tot)71-104
Aantal pagina's34
TijdschriftThe Quarterly Journal of Mathematics
Nummer van het tijdschrift1
StatusGepubliceerd - 1 mrt 2019

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34 pages

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