Final remarks on local discriminants

Serre’s formule de masse in prime degree

“…Thus they are not merely F p -spaces but kspaces (of k-dimension p − 1). The pictures in [7], §5 summarise some of these facts. PROPOSITION 29.…”

“…The proof is similar to that of lemma 16 (cf. Remark 4 and [7], §2). Now let D be in the χ-eigenspace for some character χ of G. For…”

“…There are two sources of inspiration for our method. The first one is our recent reworking [7] of a standard technique used in proofs of the local [3, p. 155] or the global [13, p. 110] Kronecker-Weber theorem. It allowed us to compute the contribution of degree-p cyclic extensions to the mass formula [7], §6.…”