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This extends work of Lichtenbaum \\cite{Lichtenbaum05} and Geisser \\cite{Geisser04b} for $\\mathcal{X}$ of characteristic $p$, of Lichtenbaum \\cite{li04} for $\\mathcal{X}=\\mathrm{Spec}(\\mathcal{O}_F)$ and $n=0$ where $F$ is a number field, and of the second author for arbitrary $\\mathcal{X}$ and $n=0$ \\cite{Morin14}. 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