Definition 14.1 ( $s$ -th ramification group). Let $v_{L}$ be a normalised valuation in $O_{L}$ . For $s \in ℝ_{\geq - 1}$ , the $s$ -th ramification group is

G_{s} (L ∕ K) = {σ \in Gal (K) | v_{L} (σ (x) - x) \geq s + 1 \forall x \in O_{L}} .