Kummer-Artin-Schreier-Witt Theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917289424584704 |
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| author | Dang, Huy Nguyen-Dang, Khai-Hoan |
| author_facet | Dang, Huy Nguyen-Dang, Khai-Hoan |
| contents | We study the problem of lifting the Artin--Schreier--Witt isogeny from characteristic $p>0$ to characteristic $0$, which is central to the lifting problem for Galois covers of algebraic schemes in positive characteristic. We introduce a new technique that associates a Kummer class, representing a tamely ramified cyclic extension, to a Witt vector via Matsuda's Kummer--Artin--Schreier--Witt theory. This viewpoint leads to an explicit construction of a lift of the isogeny over a concrete base ring. Our results lay the groundwork for further applications, including the study of inseparable extensions and Kato's refined Swan conductor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kummer-Artin-Schreier-Witt Theory Dang, Huy Nguyen-Dang, Khai-Hoan Number Theory Algebraic Geometry We study the problem of lifting the Artin--Schreier--Witt isogeny from characteristic $p>0$ to characteristic $0$, which is central to the lifting problem for Galois covers of algebraic schemes in positive characteristic. We introduce a new technique that associates a Kummer class, representing a tamely ramified cyclic extension, to a Witt vector via Matsuda's Kummer--Artin--Schreier--Witt theory. This viewpoint leads to an explicit construction of a lift of the isogeny over a concrete base ring. Our results lay the groundwork for further applications, including the study of inseparable extensions and Kato's refined Swan conductor. |
| title | Kummer-Artin-Schreier-Witt Theory |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.21224 |