A cohomology class of a smooth complex variety of dimension n has coniveau at least c if it vanishes in the complement of a closed subvariety of codimension at least c, and it has strong coniveau at least c if it comes by proper pushforward from the cohomology of a smooth variety of dimension at most . 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.
"Two coniveau filtrations." Duke Math. J. Advance Publication 1 - 35, 2021. https://doi.org/10.1215/00127094-2021-0055