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Suppose $X\in \mathrm{Sm}/k$. Is the sheaf with transfers $\mathbb{Z}_{\mathrm{tr}}(X)$ a cdh sheaf? Its sections are finite correspondences.

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    $\begingroup$ No, it is not: cdh-locally, all finite correspondences are linear combinations of Hilbert cycles (geometric correspondences that are finite and flat on the source). $\endgroup$
    – D.-C. Cisinski
    Commented Oct 31, 2022 at 8:00

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