On defect in finite extensions of valued fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913749482340352 |
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| author | de Souza, Caio Henrique Silva Spivakovsky, Mark |
| author_facet | de Souza, Caio Henrique Silva Spivakovsky, Mark |
| contents | In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify defectless fields and study properties related to defect. In this paper we study the relations between the following properties of valued fields: simply defectless, immediate-defectless and algebraically maximal. The main result of the paper is an example of an algebraically maximal field that admits a simple defect extension. For this, we introduce the notion of quasi-finite elements in the generalized power series field $k\left(\left(t^Γ\right)\right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On defect in finite extensions of valued fields de Souza, Caio Henrique Silva Spivakovsky, Mark Commutative Algebra Algebraic Geometry In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify defectless fields and study properties related to defect. In this paper we study the relations between the following properties of valued fields: simply defectless, immediate-defectless and algebraically maximal. The main result of the paper is an example of an algebraically maximal field that admits a simple defect extension. For this, we introduce the notion of quasi-finite elements in the generalized power series field $k\left(\left(t^Γ\right)\right)$. |
| title | On defect in finite extensions of valued fields |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2503.16716 |