Galois module structure of $p^{\text{th}}$ power classes of abelian extensions of local fields

Alexandre Eimer

In this paper, we describe the Galois module structure of $J={\mathbf{K}}^{\times }/{\mathbf{K}}^{\times p}$, where $\mathbf{K}$ is an extension of a local field $\mathbf{k}$ containing…