Defining coarsenings of valuations
We study the question of which Henselian fields admit definable Henselian valuations (with or without parameters). We show that every field that admits a Henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) Henselian valuation. In equicharacteristic 0, we giv...
| Main Authors: | , |
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| Format: | Journal article |
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Cambridge University Press
2017
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| _version_ | 1797056127337234432 |
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| author | Jahnke, F Koenigsmann, J |
| author_facet | Jahnke, F Koenigsmann, J |
| author_sort | Jahnke, F |
| collection | OXFORD |
| description | We study the question of which Henselian fields admit definable Henselian valuations (with or without parameters). We show that every field that admits a Henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) Henselian valuation. In equicharacteristic 0, we give a complete characterization of Henselian fields admitting a parameter-definable (non-trivial) Henselian valuation. We also obtain partial characterization results of fields admitting-definable (non-trivial) Henselian valuations. We then draw some Galois-theoretic conclusions from our results. |
| first_indexed | 2024-03-06T19:19:00Z |
| format | Journal article |
| id | oxford-uuid:196629ea-9386-43d4-8252-f352ca45ae47 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:19:00Z |
| publishDate | 2017 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:196629ea-9386-43d4-8252-f352ca45ae472022-03-26T10:48:50ZDefining coarsenings of valuationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:196629ea-9386-43d4-8252-f352ca45ae47Symplectic Elements at OxfordCambridge University Press2017Jahnke, FKoenigsmann, JWe study the question of which Henselian fields admit definable Henselian valuations (with or without parameters). We show that every field that admits a Henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) Henselian valuation. In equicharacteristic 0, we give a complete characterization of Henselian fields admitting a parameter-definable (non-trivial) Henselian valuation. We also obtain partial characterization results of fields admitting-definable (non-trivial) Henselian valuations. We then draw some Galois-theoretic conclusions from our results. |
| spellingShingle | Jahnke, F Koenigsmann, J Defining coarsenings of valuations |
| title | Defining coarsenings of valuations |
| title_full | Defining coarsenings of valuations |
| title_fullStr | Defining coarsenings of valuations |
| title_full_unstemmed | Defining coarsenings of valuations |
| title_short | Defining coarsenings of valuations |
| title_sort | defining coarsenings of valuations |
| work_keys_str_mv | AT jahnkef definingcoarseningsofvaluations AT koenigsmannj definingcoarseningsofvaluations |