Galois module structure of the integers in weakly ramified extensions

摘要

Let L/K be a finite Galois extension of local fields which are finite extensions of Q_p, the field of p-adic numbers. Let Gal (L/K) = G and let D_L, Z_p denote the rings of integers in L and Q_p, respectively. In this note, we determine, explicitly, the structure of D_L as a Z_p [G]-module for the class of weakly ramified extensions which are totally wildly ramified. An extension is said to be weakly ramified if the second ramifica tion group is trivial [2].