论文标题
增强估值和最小对
Augmented Valuation and Minimal Pair
论文作者
论文摘要
令$（k，ν）$为一个有价值的字段，是\ emph {增强估值}的概念，\ emph {lim lim lim formph {limit增强估值}和\ emph {formph {可接纳家庭}的估值，可以对任何估值$ $ $ k [x] $延长$ neftery $ n $ c $ n $ c $ c $ c $ c。如果字段$ k $是代数关闭的，则此描述特别简单，我们可以将其简化为\ emph {minimal pair}和\ emph {pseudo-convergent family}的概念。令$（k，n）$为henselian有价值的字段，$ \barν$ $ν$的唯一扩展名给代数关闭$ \ bar k $ $ k $ of $ k $ of $ k $ of $ k $ of $ k $ of $ k $ of $ k $ of $ k $ of $ k $的估值是$ k [x] $扩展$ν$的估值$ \barμ_i$的$ \ bar k [x] $，是估值的扩展$μ_i$，属于与$μ$相关的可允许家族。
Let $(K, ν)$ be a valued field, the notions of \emph{augmented valuation}, of \emph{limit augmented valuation} and of \emph{admissible family} of valuations enable to give a description of any valuation $μ$ of $K [x]$ extending $ν$. In the case where the field $K$ is algebraically closed, this description is particularly simple and we can reduce it to the notions of \emph{minimal pair} and \emph{pseudo-convergent family}. Let $(K, ν)$ be a henselian valued field and $\barν$ the unique extension of $ν$ to the algebraic closure $\bar K$ of $K$ and let $μ$ be a valuation of $ K [x]$ extending $ν$, we study the extensions $\barμ$ from $μ$ to $\bar K [x]$ and we give a description of the valuations $\barμ_i$ of $\bar K [x]$ which are the extensions of the valuations $μ_i$ belonging to the admissible family associated with $μ$.
