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Thanks to Yijin Wang https://stacks.math.columbia.edu/tag/03GZ#comment-7357 Typo in lemma 37.52.3: In the forth line 'we see that X_s×Spec(κ(s) Spec(k) is disconnected ' should be 'we see that X_s×Spec(κ(s)) Spec(k) is disconnected '
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