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

Autor:	Thatte, Vaidehee
Rok vydání:	2024
Předmět:	Mathematics - Commutative Algebra Mathematics - Number Theory 11S15 13A18
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.01825 Zobrazit plný text záznamu View this record from Arxiv