All Questions

In Serre's book "Local fields" he defines the function $\phi(u)=\int_{0}^{u}\frac{dt}{( G_0:G_t)}$ and defines the upper number of ramification groups as $G^v=G_{\phi^{-1}(v)}$ and somehow ...

Given a local field $K$ with absolute Galois group $\Gamma$. Is it "possible" to define the upper numbering on $\Gamma$ without using the lower numbering? In other words, given $\gamma \in \...

Let $K$ be an unramified extension of the $p$-adic number field $\mathbb{Q}_p$. Suppose we have a tower of extensions: $$K=:K(u_0) \subset K(u_1) \subset K(u_2) \subset K(u_3) \subset \cdots \subset ...