On functions given by algebraic power series over Henselian valued fields

This paper provides, over Henselian valued fields, some theorems on implicit function and of Artin--Mazur on algebraic power series. Also discussed are certain versions of the theorems of Abhyankar--Jung and Newton--Puiseux. The latter is used in analysis of functions of one variable, definable in t...

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Bibliographic Details
Published in:arXiv.org 2017-03
Main Author: Nowak, Krzysztof Jan
Format: Article
Language:English
Subjects:
Algebra
Existence theorems
Mathematical analysis
Power series
Online Access:Get full text
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Summary:This paper provides, over Henselian valued fields, some theorems on implicit function and of Artin--Mazur on algebraic power series. Also discussed are certain versions of the theorems of Abhyankar--Jung and Newton--Puiseux. The latter is used in analysis of functions of one variable, definable in the language of Denef--Pas, to obtain a theorem on existence of the limit, proven over rank one valued fields in one of our recent papers. This result along with the technique of fiber shrinking (developed there over rank one valued fields) were, in turn, two basic tools in the proof of the closedness theorem.
ISSN:2331-8422