论文标题
将密钥多项式限制为$ p $ - 多项式元素
Limit key polynomials as $p$-polynomials
论文作者
论文摘要
本文的主要目的是表征$ k [x] $的估值$ν$的限制密钥多项式。我们考虑$ n $ $α$的$ν$的键多项式的$ψ_α$。我们将$ p $设置为$ν$的指数特征。我们的第一个主要结果（定理1.1）是，如果$q_α$是$ψ_α$的限制密钥多项式，则$q_α$的度数为$ p^rα$，对于某些$ r \ in \ mathbb n $。此外，在定理1.2中，我们表明存在$ q \inψ_α$和$q_α$ limit限制$ψ_α$的限制键多项式，因此，$ q $ q $q_α$仅具有$ p $的功率。
The main goal of this paper is to characterize limit key polynomials for a valuation $ν$ on $K[x]$. We consider the set $Ψ_α$ of key polynomials for $ν$ of degree $α$. We set $p$ be the exponent characteristic of $ν$. Our first main result (Theorem 1.1) is that if $Q_α$ is a limit key polynomial for $Ψ_α$, then the degree of $Q_α$ is $p^rα$ for some $r\in\mathbb N$. Moreover, in Theorem 1.2, we show that there exist $Q\inΨ_α$ and $Q_α$ a limit key polynomial for $Ψ_α$, such that the $Q$-expansion of $Q_α$ only has terms which are powers of $p$.
