Multivariate Hensel Lemma for ultrametric fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911780810260480 |
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| author | Alonso, M. -E. Lombardi, H. Neuwirth, S. |
| author_facet | Alonso, M. -E. Lombardi, H. Neuwirth, S. |
| contents | The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situation that is a priori much more difficult. In this paper, we give a direct proof of the Multivariate Hensel Lemma for ultrametric fields, in the framework of constructive mathematics and without using~ZMT. In the framework of classical mathematics, our result entails the Lemma for rank-one valued fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_06546 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multivariate Hensel Lemma for ultrametric fields Alonso, M. -E. Lombardi, H. Neuwirth, S. Commutative Algebra 13B40, 13J15, 03F65 The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situation that is a priori much more difficult. In this paper, we give a direct proof of the Multivariate Hensel Lemma for ultrametric fields, in the framework of constructive mathematics and without using~ZMT. In the framework of classical mathematics, our result entails the Lemma for rank-one valued fields. |
| title | Multivariate Hensel Lemma for ultrametric fields |
| topic | Commutative Algebra 13B40, 13J15, 03F65 |
| url | https://arxiv.org/abs/2301.06546 |