p-Groupes abéliens de type (p,…,p) et disques ouverts p-adiques

Abstract:

Let k be an algebraically closed field of characteristic p>0, W(k) its ring of Witt vectors and R a complete discrete valuation ring dominating W(k). Consider finite groups G≃ (ℤ/pℤ)ⁿ, p≥ 2, n≥1. In a former paper we showed that a given realization of such a G as a group of k-automorphisms of k[[z]] must satisfy some conditions in order to have a lifting as a group of R-automorphisms of R[[Z]]. In this note, we give for every G (all p≥ 2, n>1) a realization as an automorphism group of k[[z]] which ca be lifted as a group of R-automorphisms of R[[Z]] for suitable R.