Split embedding problems over complete domains

• 成果类型: Article
• 署名作者: Paran, Elad
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.899
• 发表日期: 2009
• 页码: 899-914
• 关键词: complete valued fields; galois-groups; abhyankars conjecture

摘要

We prove that every finite split embedding problem is solvable over the field K((X-1,..., X-n)) of formal power series in n >= 2 variables over an arbitrary field K, as well as over the field Quot(A [[X-1,..., 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((X-1, X-2)).