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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)).

Split embedding problems over complete domains