Also appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

I will propose an effective axiomatization for ℚªᵇ_p, the maximal abelian extension of the p-adics, and present a strategy for proving quantifier elimination (in a variant of the Macintyre language) for the theory thus axiomatized. This should eventually give the decidability of ℚªᵇ_p and all its finite extensions.