Definable henselian valuations in positive residue characteristic
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917071809413120 |
|---|---|
| author | Ketelsen, Margarete Ramello, Simone Szewczyk, Piotr |
| author_facet | Ketelsen, Margarete Ramello, Simone Szewczyk, Piotr |
| contents | We study the question of $\mathcal{L}_{\mathrm{ring}}$-definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Definable henselian valuations in positive residue characteristic Ketelsen, Margarete Ramello, Simone Szewczyk, Piotr Logic Commutative Algebra 03C60, 12L12 We study the question of $\mathcal{L}_{\mathrm{ring}}$-definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields. |
| title | Definable henselian valuations in positive residue characteristic |
| topic | Logic Commutative Algebra 03C60, 12L12 |
| url | https://arxiv.org/abs/2401.06884 |