Completions of valuation rings
Completions of valuation rings
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评估环的完成
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
L. Ghezzi
中科院分区：
文献类型：
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作者：
S. Cutkosky;L. Ghezzi
设k是特征为零的域，K是k上的代数函数域，V是K的k-赋值环。Zebrski的局部一致化定理证明了存在商域K被V控制的代数正则局部环R_i，使得R_i的直并为V.本文研究了R_i的完备化的直并环T.给出了T是赋值环的充要条件。然后，我们专注于估值为1的情况。
Let k be a field of characteristic zero, K an algebraic function field over k, and V a k-valuation ring of K. Zariski's theorem of local uniformization shows that there exist algebraic regular local rings R_i with quotient field K which are dominated by V, and such that the direct union of the R_i's is V. We investigate the ring T, which is the direct union of the completions of the R_i's. We give necessary and sufficient conditions for T to be a valuation ring. We then focus on the case in which the valuation has rank one.