On complete intersections in varieties with finite-dimensional motive

2017/09/29 by Laterveer, Robert, Nagel, Jan, Peters, Chris
#14C15 #14C25 #14C30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.10259

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) → H_2k(X) are injective for k

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