Let $K$ be a $p$-adic local field, for example $\mathbb{Q}_p$. Let $G$ be the absolute Galois group of $K$, and let $G^v$($v\ge -1$) be the ramification groups in upper numbering, then is it true that $\bigcap_{v=0}^\infty G^v=\{0\}$?
Is the intersection of ramification groups in upper numbering of a $p$-adic local field trivial?
Bonbon
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