  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 root of 1; the case
of other local fields with finite residue fields was treated earlier. In all
cases, we compute the contribution of cyclic extensions to Serre's degree-$p$
mass formula.

Number Theory