论文标题
Hensel最小性：$ \ ell $ -H-MINIMITH的几何标准
Hensel minimality: Geometric criteria for $\ell$-h-minimality
论文作者
论文摘要
最近，Cluckers，Halupczok和Rideau-Kikuchi开发了一个新的公理框架，用于驯服的非Archimedean几何形状，称为Hensel最小值。它与作者一起扩展到混合特征。 Hensel最小值旨在模仿强大后果和广泛适用性的O最小性。在本文中，我们继续研究Hensel最小值，特别是专注于$ω$ -H-MINIMITAL和$ \ ell $ -H-MINIMATIE，以$ \ ell $ a正整数。我们的主要结果包括用于$ \ ell $ -H-MINIMALITY的分析标准，在估值调整下保存$ \ ell $ -h -Inimimal和$ \ ell $ - 维尺寸的几何形状。
Recently, Cluckers, Halupczok and Rideau-Kikuchi developed a new axiomatic framework for tame non-Archimedean geometry, called Hensel minimality. It was extended to mixed characteristic together with the author. Hensel minimality aims to mimic o-minimality in both strong consequences and wide applicability. In this article, we continue the study of Hensel minimality, in particular focusing on $ω$-h-minimality and $\ell$-h-minimality, for $\ell$ a positive integer. Our main results include an analytic criterion for $\ell$-h-minimality, preservation of $\ell$-h-minimality under coarsening of the valuation and $\ell$-dimensional dimensional geometry.
