Hensel minimality: Geometric criteria for $\ell$-h-minimality
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913183388663808 |
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| author | Vermeulen, Floris |
| author_facet | Vermeulen, Floris |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04158 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hensel minimality: Geometric criteria for $\ell$-h-minimality Vermeulen, Floris Logic 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. |
| title | Hensel minimality: Geometric criteria for $\ell$-h-minimality |
| topic | Logic |
| url | https://arxiv.org/abs/2204.04158 |