Split embedding problems over complete domains

Abstract

We prove that every finite split embedding problem is solvable over the field K((X1, ..., Xn)) of formal power series in n ≥ 2 variables over an arbitrary field K, as well as over the field Quot.A[[X1, ..., Xn]] of formal power series in n ≥ 1 variables over a Noetherian integrally closed domain A. This generalizes a theorem of Harbater and Stevenson, who settled the case K((X1, X2)).