Key polynomials for simple extensions of valued fields

Journal of Singularities
volume 25 (2022), 197-267

Received: 26 December 2020. Received in revised form: 28 May 2022.

DOI: 10.5427/jsing.2022.25k

Add a reference to this article to your citeulike library.

Abstract:

In this paper we present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e and reminiscent of approximate roots of Abhyankar and Moh. Given a simple transcendental extension of valued fields, we associate to it a countable well-ordered set of polynomials called key polynomials. We define limit key polynomials and give explicit formulae for them. We give an explicit bound on the order type of the set of key polynomials.

Author(s) information:

J. Herrera Govantes
Departamento de Álgebra
Facultad de Matemáticas
Avda. Reina Mercedes, s/n, Universidad de Sevilla
41012 Sevilla, Spain
jherrera@algebra.us.es

W. Mahboub
Institut de Mathématiques de Toulouse
UMR 5219 du CNRS
Université Paul Sabatier, 118, route de Narbonne
31062 Toulouse cedex 9, France
wael.mahboub@math.univ-toulouse.fr

M. A. Olalla Acosta
Departamento de Álgebra
Facultad de Matemáticas
Avda. Reina Mercedes, s/n, Universidad de Sevilla
41012 Sevilla, Spain
miguelolalla@us.es

M. Spivakovsky
Institut de Mathématiques de Toulouse
UMR 5219 du CNRS
Université Paul Sabatier, 118, route de Narbonne
31062 Toulouse cedex 9, France
and
UMI CNRS 2001 LaSol, UNAM
mark.spivakovsky@math.univ-toulouse.fr