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Article Dans Une Revue Quarterly Journal of Mathematics Année : 2019

On complete intersections in varieties with finite-dimensional motive

Résumé

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.

Dates et versions

hal-02174842 , version 1 (05-07-2019)

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Citer

Robert Laterveer, Jan Nagel, Chris Peters. On complete intersections in varieties with finite-dimensional motive. Quarterly Journal of Mathematics, 2019, 70 (1), pp.71-104. ⟨10.1093/qmath/hay038⟩. ⟨hal-02174842⟩
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