On the implicit constant fields and key polynomials for valuation algebraic extensions

Pub Date : 2021-11-29 DOI:10.1216/jca.2022.14.515
Arpan Dutta
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引用次数: 2

Abstract

This article is a natural continuation of our previous works [7] and [6]. In this article, we employ similar ideas as in [4] to provide an estimate of IC(K(X)|K, v) when (K(X)|K, v) is a valuation algebraic extension. Our central result is an analogue of [6, Theorem 1.3]. We further provide a natural construction of a complete sequence of key polynomials for v over K in the setting of valuation algebraic extensions.
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关于估值代数扩展的隐式常数域和关键多项式
本文是我们之前的工作[7]和[6]的自然延续。在本文中,我们采用与[4]中类似的思想来提供当(K(X)|K, v)是估值代数扩展时IC(K(X)|K, v)的估计。我们的中心结果类似于[6,定理1.3]。在赋值代数扩展的情况下,我们进一步给出了v / K的键多项式完全序列的自然构造。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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