Degree $p$ Extensions of Arbitrary Valuation Rings and "Best $f$"
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909157339168768 |
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| author | Thatte, Vaidehee |
| author_facet | Thatte, Vaidehee |
| contents | We prove the explicit characterization of the so-called "best f" for degree $p$ Artin-Schreier and degree $p$ Kummer extensions of Henselian valuation rings in residue characteristic $p$. This characterization is mentioned briefly in [Th16, Th18]. Existence of best $f$ is closely related to the defect of such extensions and this characterization plays a crucial role in understanding their intricate structure. We also treat degree $p$ Artin-Schreier defect extensions of higher rank valuation rings, extending the results in [Th16], and thus completing the study of degree $p$ extensions that are the building blocks of the general theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degree $p$ Extensions of Arbitrary Valuation Rings and "Best $f$" Thatte, Vaidehee Commutative Algebra Number Theory 11S15, 13A18 We prove the explicit characterization of the so-called "best f" for degree $p$ Artin-Schreier and degree $p$ Kummer extensions of Henselian valuation rings in residue characteristic $p$. This characterization is mentioned briefly in [Th16, Th18]. Existence of best $f$ is closely related to the defect of such extensions and this characterization plays a crucial role in understanding their intricate structure. We also treat degree $p$ Artin-Schreier defect extensions of higher rank valuation rings, extending the results in [Th16], and thus completing the study of degree $p$ extensions that are the building blocks of the general theory. |
| title | Degree $p$ Extensions of Arbitrary Valuation Rings and "Best $f$" |
| topic | Commutative Algebra Number Theory 11S15, 13A18 |
| url | https://arxiv.org/abs/2404.01825 |