Normalization for \({\mathfrak p}\)-adic fields. I (Q1901843)

Let \(K\) be a complete field of characteristic zero with an arbitrary residue class field of characteristic \(p\). A standard field is a field of the form \(kK_0\), where \(K_0\) is unramified over \(\mathbb{Q}_p\) and \(k\) is a finite extension of a subfield \(k_0\) of \(K_0\) with separable residue field. The author shows that there exists a finite extension of \(K\) which is standard. His main result is a nice description of all \(\Gamma\)-extensions of \(K\).