Effective estimation of integer points of a family of algebraic curves
type: Item
instance of: scholarly article
title: Effective estimation of integer points of a family of algebraic curves
zbMATH Open document ID: 0879.11030
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1997-11-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73400
review text: If \(X\), \(Y\), \(Z\) are affine algebraic curves defined over a number field, with \(Y,Z\) covers of \(X\) and \(Z/X\) unramified, then integral points on \(Y\) map to integral points on \(X\) and those lift to integral points on \(Z\) perhaps after base field extension. The author has a simple geometric criterion on a plane curve \(Y\), which allows him to find \(X\) and \(Z\) as above, in such a way that \(Z\) is a curve where it is known how to find the integral points (for example an elliptic curve). In this way he obtains an effective bound for the integral points on the curves that satisfy his criterion. The main result improves ealier work of \textit{Yu. F. Belotserkovskij} [Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 1988, No. 6, 34-39 (1988; Zbl 0669.10037)].
Mathematics Subject Classification ID: 11G30
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 1051571
zbMATH Keywords: integral points
zbMATH Keywords: algebraic curves
author: Dimitros Poulakis
reviewed by: José Felipe Voloch
MaRDI profile type: Publication
OpenAlex ID: W2332061997
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DOI: 10.5802/AFST.845
description: scientific article; zbMATH DE number 1051571