ON SATURATED DISTINGUISHED CHAINS OVER A LOCAL FIELD III: The Case of p-Extensions with Two Proper Higher Ramification Groups

Abstract

This is a continuation of the papers [5, 6] on saturated distinguished chains (SDCs) over a local field K. We consider a totally ramified Galois extension L of K whose Galois group is a p-group and has exactly two proper higher ramification groups, where p is the characteristic of the residual field. Take a prime element π of L, and set πi = NL/Mi(π), where Mi are the corresponding fields to higher ramification groups such that K ⊂ M1 ⊂ M2 ⊂ L and NL/Mi denotes the norm map from L to Mi for each i. We consider a SDC for α = π1 + π1π2 + π1π2π over K, and the result is given as Main Theorem. There are thirteen cases according to sizes of extension degrees [L : M2], [M2 : M1] and [M1 : K].