On a Characterization of the First Ramification Group as the Vertex of the Ring of Integers

Abstract

Introduction.Let k be a p-adic number field and o be the ring of all integers in k. Moreover, let K\k be a finite Galois extension with the Galois group G = G{Kjk). Then the ring D of all integers in K is an o[G]-module. In this paper we shall give a characterization of the first ramification group G x of the extension Kjk as the vertex of £> which is defined below.To define the vertex of £>, we remember the vertex theory (