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arXiv · 2404.01825

Degree $p$ Extensions of Arbitrary Valuation Rings and "Best $f$"

Vaidehee Thatte
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Abstract

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.

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Vaidehee Thatte. 2024-04-02. Degree $p$ Extensions of Arbitrary Valuation Rings and "Best $f$". https://arxiv.org/abs/2404.01825

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