On MacLane-Vaqui\'e key polynomials

TL;DR

This paper explores the relationship between limit key polynomials and limit MacLane-Vaquié key polynomials, extending previous work and generalizing several existing results in valuation theory.

Contribution

It establishes the connection between limit key polynomials and limit MacLane-Vaquié key polynomials, generalizing prior results in the field.

Findings

Established the relation between limit key polynomials and limit MacLane-Vaquié key polynomials.

Generalized several existing results in valuation theory.

Extended previous work by Decaup, Mahboub, and Spivakovsky.

Abstract

One of the main goals of this paper is to present the relation of limit key polynomials and limit MacLane-Vaqui\'e key polynomials. This is a continuation of the work started in a paper by Decaup, Mahboub and Spivakovsky, where it is proved the equivalent result for key polynomials (which are not limit). Moreover, we present a result (Theorem 1.1) that generalizes various results in the literature.