Final Remarks on Local Discriminants

We show how the ramification filtration on the maximal elementary abelian p-extension (p prime) on a local number field of residual characteristic p can be derived using only Kummer theory and a certain orthogonality relation for the Kummer pairing, even in the absence of a primitive p-th ischolar_main of 1; the case of other local fields was treated earlier. In all cases, we compute the contribution of cyclic extensions to Serre’s degree-p mass formula.