# Looking for proof of Serre's mass formula

Let $$F$$ be a finite field extension of the $$p$$-adic numbers $$\mathbb{Q}_p$$, whose residue field has $$q$$ elements. Let $$\mathfrak{p}$$ be the prime ideal of $$F$$. Given a finite field extension $$K/F$$, write $$\operatorname{Disc}_\mathfrak{p}(K)$$ for $$q^{v_\mathfrak{p}(\operatorname{Disc}(K/F))}$$. Then Serre's mass formula states that for all $$n\geq 1$$, we have

$$\sum_{[K:F] = n \text{ totally ramified}} \frac{1}{\#\operatorname{Aut}(K/F)}\cdot\frac{1}{\operatorname{\operatorname{Disc}_{\mathfrak{p}}(K)}} = \frac{1}{q^{n-1}}.$$

This result first appeared in Serre's 1978 paper Une “ formule de masse ” pour les extensions totalement ramifiees de degre donne d’un corps local. As far as I can tell, this paper is only available in the book Oeuvres/Collected Papers. 3 volumes. Given that I am unable to obtain this book, I am looking for a reference on the internet that contains either Serre's original paper or an exposition of his proof (ideally both proofs from the paper).

I would also (delightedly) accept an answer that directly explains the proof (i.e. no reference); such an answer would in my opinion be a great addition to the learning resource that is MO, seeing as the proof is so hard to find on the internet!