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arXiv · 2410.21224

Kummer-Artin-Schreier-Witt Theory

Huy Dang·Khai-Hoan Nguyen-Dang
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Abstract

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.

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BibTeXRIS

Huy Dang, Khai-Hoan Nguyen-Dang. 2024-10-28. Kummer-Artin-Schreier-Witt Theory. https://arxiv.org/abs/2410.21224

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