阿尔廷-施莱尔扩展与亨塞尔有价域的组合复杂性

BLAISE BOISSONNEAU
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引用次数: 0

摘要

我们给出了在具有阿尔廷-施赖尔扩展的域中见证 IP、IP$_{\!n}$ 或 TP2 的明确公式。我们用它们来控制混合特征亨氏有价域的 p 扩展,这使我们得以将安斯康伯-雅克对 NIP 亨氏有价域的一种分类方法推广到 NIP$_{\!n}$ 范畴。作为推论,我们得到具有 NIP 残差域的 NIP$_{\!n}$ henselian 有价域是 NIP 的。我们还讨论了 NTP2 henselian 有价域的驯化结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
ARTIN–SCHREIER EXTENSIONS AND COMBINATORIAL COMPLEXITY IN HENSELIAN VALUED FIELDS

We give explicit formulas witnessing IP, IP$_{\!n}$, or TP2 in fields with Artin–Schreier extensions. We use them to control p-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP$_{\!n}$ context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP$_{\!n}$ henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.

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