Valuations in fields of power series

This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of power series in two and three variables, according to their re...

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Bibliographic Details
Published in:arXiv.org 2002-12
Main Authors: Herrera-Govantes, F J, Olalla Acosta, M A, Vicente-Cordoba, J L
Format: Article
Language:English
Subjects:
Meromorphic functions
Power series
Online Access:Get full text
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Summary:This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of power series in two and three variables, according to their residue fields. We prove that all our cases are possible and give explicit constructions.
ISSN:2331-8422
DOI:10.48550/arxiv.0212203