分野別セミナー

Serre had proved a beautiful mass formula involving all totally ramified extensions of a given degree over a local field (with finite residue field). We give various refinements of this formula in prime degree, computing the mass of various kinds of totally ramified extensions, for example those which are galoisian, or become galoisian over some given extension, etc. This is achieved by finding a canonical parametrisation of all separable extensions of prime degree, preserving the structures involved, including the ramification.