Two coniveau filtrations

A class in the cohomology of a smooth $n$-dimensional variety has coniveau $\ge c$ if it vanishes in the complement of a subvariety of dimension $n-c$, and has strong coniveau $\ge c$ if it comes by proper pushforward from the cohomology of a smooth variety of dimension $n-c$. I will present examples showing that these two filtrations differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties. This is joint work with John Ottem.
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