Indices of inseparability for elementary abelian \(p\)-extensions (Q2637187)

Let \(K\) be a local field whose residue field \(\bar{K}\) is a finite field of characteristic \(p\) and let \(L/K\) be a finite totally ramified Galois extension. \textit{M. Fried} [Acta Arith. 25, 225--258 (1974; Zbl 0229.12020)] and \textit{V. Heiermann} [J. Number Theory 59, No. 1, 159--202 (1996; Zbl 0876.11053)] defined the ``indices of inseparability'' of \(L/K\), a refinement of the ramification data of \(L/K\). In this paper the author gives a method for computing the indices of inseparability of the extension \(L/K\) in terms of the norm group \(N_{L/K}(L^\times)\) in the case where \(K\) has characteristic \(p\) and \(\mathrm{Gal} (L/K)\) is an elementary abelian \(p\)-group with a single ramification break. In some cases these methods lead to simple formulas for the indices of inseparability.