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arXiv · 1403.3904

The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II

Claire Voisin
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Abstract

We prove an unconditional (but slightly weakened) version of the main result of our earlier paper with the same title, 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 $CH(X)_\mathbb{Q}$). We prove that if the cohomology of a general very ample hypersurface $Y$ in $X$ is ``parameterized by cycles of dimension $c$'', then the Chow groups $CH_{i}(Y)_\mathbb{Q}$ are trivial for $i\leq c-1$.

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Claire Voisin. 2014-03-16. The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II. https://arxiv.org/abs/1403.3904

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