AKE principles for deeply ramified fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914434358706176 |
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| author | Jahnke, Franziska van der Schaaf, Jonas |
| author_facet | Jahnke, Franziska van der Schaaf, Jonas |
| contents | We study the model theory of deeply ramified fields of positive characteristic. Generalizing the perfect case treated in work by Jahnke and Kartas on the model theory of perfectoid fields, we obtain Ax-Kochen/Ershov principles for certain deeply ramified fields of positive characteristic and fixed degree of imperfection. Our results apply in particular to all deeply ramified henselian valued fields of rank 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | AKE principles for deeply ramified fields Jahnke, Franziska van der Schaaf, Jonas Logic Commutative Algebra 12L12 03C60 12J10 We study the model theory of deeply ramified fields of positive characteristic. Generalizing the perfect case treated in work by Jahnke and Kartas on the model theory of perfectoid fields, we obtain Ax-Kochen/Ershov principles for certain deeply ramified fields of positive characteristic and fixed degree of imperfection. Our results apply in particular to all deeply ramified henselian valued fields of rank 1. |
| title | AKE principles for deeply ramified fields |
| topic | Logic Commutative Algebra 12L12 03C60 12J10 |
| url | https://arxiv.org/abs/2603.29528 |