Year: 2022
Type: preprint
Abstract: In this paper we present a characterization for the defect of a simple algebraic extensions of valued fields. This characterization generalizes the known result for the henselian case, namely that the defect is the product of the relative degrees of limit augmentations. The main tool used here is the graded algebra associated to a valuation on a polynomial ring. Let $\kh$ be a henselization of a valued field $K$. Another relevant result proved in this paper is that for every valuation $\muh$ on $\khx$, with restriction $μ$ on $\kx$, the corresponding map $\mathcal G_μ\hk\mathcal G_{\muh}$ of graded algebras is an isomorphism.
Source: arXiv (Cornell University)
Authors: Novacoski, Josnei, Nart, Enric
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1264927793, G1365296122, G6438247056
OpenAlex ID: W4288043119