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

2024/04/02 by Vaidehee Thatte, Thatte, Vaidehee
Mathematics · #11S15 #13A18 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2404.01825

openalex publication_date 2024/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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