Quelques "formules de masse" raffin\'ees en degr\'e premier

TL;DR

This paper refines Serre's mass formula for degree p extensions over local fields, enabling detailed computations of contributions from cyclic extensions, specific Galois groups, and prescribed ramification properties.

Contribution

It introduces refined formulas that allow precise calculation of extension contributions based on Galois group and ramification data, extending Serre's original mass formula.

Findings

Refined formulas for cyclic extensions

Calculations for Galois groups and automorphisms

Extensions with specified ramification properties

Abstract

For a local field with finite residue field of characteristique p, we give some refinements of Serre's mass formula in degree p which allow us to compute for example the contribution of cyclic extensions, or of those whose galoisian closure has a given group as group of automorphisms, or has ramification properties given in advance.