TY - JOUR

T1 - Split embedding problems over complete domains

AU - Paran, Elad

PY - 2009

Y1 - 2009

N2 - 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)).

AB - 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)).

UR - http://www.scopus.com/inward/record.url?scp=71449087074&partnerID=8YFLogxK

U2 - 10.4007/annals.2009.170.899

DO - 10.4007/annals.2009.170.899

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AN - SCOPUS:71449087074

SN - 0003-486X

VL - 170

SP - 899

EP - 914

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -