Take a smooth proper morphism of schemes $X\to S$. Fix a point $t\in S$ and a point $s\in \overline\{s\}$. For a prime $l$ which is invertible in $S$, is there the natural specialization map of etale K theory $$ K^{{\acute{e}}t}(X_{\overline{s}})^{\wedge}_l \to K^{{\acute{e}}t}(X_{\overline{t}})^{\wedge}_l? $$
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$\begingroup$ Did you intend to write that one of $s$ or $t$ is in the closure of the singleton set of the other element? That is not what you wrote above. $\endgroup$– Jason StarrCommented Sep 14, 2022 at 15:00

$\begingroup$ Where you wrote $s\in\overline\{s\}$, might you have intended $s\in\overline{\{s\}}$? $\qquad$ $\endgroup$– Michael HardyCommented Sep 17, 2022 at 2:13

$\begingroup$ $\ldots$ or $s\in\overline{\{t\}}$? $\qquad$ $\endgroup$– Michael HardyCommented Sep 17, 2022 at 2:18
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