Abstract
We prove an unconditional (but slightly weakened) version of the main result of (13), which was, starting from dimension 4, conditional to the Lefschetz standard conjecture. Let X be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on CH(X)Q). We prove that if the cohomology of a general hypersurface Y in X is parameterized by cycles of dimension c, then the Chow groups CHi(Y )Q are trivial for i ≤ c − 1.
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