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arXiv · 2003.02199

Two coniveau filtrations

Olivier Benoist·John Christian Ottem
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Abstract

A cohomology class of a smooth complex variety of dimension $n$ has coniveau $\geq c$ if it vanishes in the complement of a closed subvariety of codimension $\geq c$, and has strong coniveau $\geq c$ if it comes by proper pushforward from the cohomology of a smooth variety of dimension $\leq n-c$. We show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties.

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Olivier Benoist, John Christian Ottem. 2020-03-04. Two coniveau filtrations. https://doi.org/10.1215/00127094-2021-0055

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