Associated orders of certain extensions arising from Lubin-Tate formal groups

Abstract

Let k be a finite extension of ℚ p , let k 1 , respectively k 3 , be the division fields of level 1, respectively 3, arising from a Lubin-Tate formal group over k, and let Γ= Gal(k 3 /k 1 ). It is known that the valuation ring k 3 cannot be free over its associated order 𝔄 in KΓ unless k=ℚ p . We determine explicitly under the hypothesis that the absolute ramification index of k is sufficiently large.