Submission date: 8 April 2022

Abstract:

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 l-h-minimality, for l a positive integer. Our main results include an analytic criterion for l-h-minimality, preservation of $\ell$-h-minimality under coarsening of the valuation and l-dimensional dimensional geometry.

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Full text arXiv 2204.04158: pdf, ps.