Depth of Artin-Schreier defect towers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910890332258304 |
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| author | Nart, Enric Novacoski, Josnei |
| author_facet | Nart, Enric Novacoski, Josnei |
| contents | The depth of a simple algebraic extension $(L/K,v)$ of valued fields is the minimal length of the Mac Lane-Vaquié chains of the valuations on $K[x]$ determined by the choice of different generators of the extension. In a previous paper, we characterized the defectless unibranched extensions of depth one. In this paper, we analyze this problem for towers of Artin-Schreier defect extensions. Under certain conditions on $(K,v)$, we prove that the towers obtained as the compositum of linearly disjoint defect Artin-Schreier extensions of $K$ have depth one. We conjecture that these are the only depth one Artin-Schreier defect towers and we present some examples supporting this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Depth of Artin-Schreier defect towers Nart, Enric Novacoski, Josnei Commutative Algebra The depth of a simple algebraic extension $(L/K,v)$ of valued fields is the minimal length of the Mac Lane-Vaquié chains of the valuations on $K[x]$ determined by the choice of different generators of the extension. In a previous paper, we characterized the defectless unibranched extensions of depth one. In this paper, we analyze this problem for towers of Artin-Schreier defect extensions. Under certain conditions on $(K,v)$, we prove that the towers obtained as the compositum of linearly disjoint defect Artin-Schreier extensions of $K$ have depth one. We conjecture that these are the only depth one Artin-Schreier defect towers and we present some examples supporting this conjecture. |
| title | Depth of Artin-Schreier defect towers |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2503.18827 |