Work

Minimal limit key polynomials

Year: 2025

Type: article

Abstract: In this paper, we extend the theory of minimal limit key polynomials of valuations on the polynomial ring . Minimal key polynomials are useful to describe, for instance, the defect of an extension of valued fields. We use the theory of cuts on ordered abelian groups to show that the previous results on bounded sets of key polynomials of rank one valuations extend to vertically bounded sets of key polynomials of valuations of an arbitrary rank. We also discuss properties of minimal limit key polynomials in the vertically unbounded case.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70162

Authors: Enric Nart, Josnei Novacoski

Institutions: Universitat Autònoma de Barcelona, Universidade Federal de São Carlos

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Agencia Estatal de Investigación