论文标题
极限密钥多项式的不变性
Invariants of limit key polynomials
论文作者
论文摘要
让$ν$成为多项式环$ k [x] $的任意等级的估值，并在字段$ k $中具有系数。我们证明了估计$μ\leν$的Maclane-Vaquié密钥多项式与$ν$的抽象密钥多项式之间的比较定理。 同样，还获得了限制关键多项式的连接的一些不变性结果。特别是，如果$ \ operatorname {char}（k）= 0 $，我们表明，无界连续的麦克莱恩链的所有限制密钥多项式具有等于一个的数值字符。
Let $ν$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with coefficients in a field $K$. We prove comparison theorems between MacLane-Vaquié key polynomials for valuations $μ\leν$ and abstract key polynomials for $ν$. Also, some results on invariants attached to limit key polynomials are obtained. In particular, if $\operatorname{char}(K)=0$ we show that all limit key polynomials of unbounded continuous MacLane chains have numerical character equal to one.
