论文标题
驯服密钥多项式
Tame Key polynomials
论文作者
论文摘要
我们引入了一种新的方法，用于构建关键多项式的完整序列，以简单地扩展温和字段。在我们的方法中，关键的多项式被认为是在其代数闭合中适当构造元件的基础场上的最小多项式，它们产生的扩展形成了增加的链。在代数扩展的情况下，我们将结果推广到远高于Henselian的无限驯服扩展，但不一定是驯服场。在先验扩展的情况下，我们证明了隐式恒定场扮演的核心作用，这揭示了与代数情况的紧密联系。
We introduce a new method of constructing complete sequences of key polynomials for simple extensions of tame fields. In our approach the key polynomials are taken to be the minimal polynomials over the base field of suitably constructed elements in its algebraic closure, with the extensions generated by them forming an increasing chain. In the case of algebraic extensions, we generalize the results to countably generated infinite tame extensions over henselian but not necessarily tame fields. In the case of transcendental extensions, we demonstrate the central role that is played by the implicit constant fields, which reveals the tight connection with the algebraic case.
