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Conjugation action of $Gal(\bar{s}/s)$ on the tame ramification group
There is a statement in SGA 7-1 Exposé 1 (P. Deligne, Résumé des premiers exposés de A. Grothendieck, pdf of SGA7-1), (0.3.1):
$S$ is a Henselian trait (i.e. the spectrum of a henselian discrete ...
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