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arXiv · 1709.10259

On complete intersections in varieties with finite-dimensional motive

Robert Laterveer·Jan Nagel·Chris Peters
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Abstract

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 $A_k(X) \to H_{2k}(X)$ are injective for $k<c$. We give variants involving group actions which lead to several new examples with finite dimensional Chow motives.

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Robert Laterveer, Jan Nagel, Chris Peters. 2017-09-29. On complete intersections in varieties with finite-dimensional motive. https://arxiv.org/abs/1709.10259

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