The Siegel theorem on Diophantine equations
type: Item
instance of: scholarly article
title: The Siegel theorem on Diophantine equations
zbMATH Open document ID: 0736.11072
author: Alain Robert
published in: Expositiones Mathematicae
publication date: 1992-06-25T00:00:00Z
review text: This is a largely expository paper. Siegel's theorem states that certain affine curves have only finitely many integral points over any given subring of \(\bar\mathbb{Q}\) of finite type over \(\mathbb{Z}\). This paper presents the proof of this theorem, assuming Roth's theorem, from the point of view of nonstandard analysis: cf. \textit{A. Robinson} and \textit{P. Roquette} [J. Number Theory 7, 121-176 (1975; Zbl 0299.12107)]. The exposition is elementary except that, as the author notes, increasing amounts of algebraic geometry are needed as the exposition progresses. The paper also assumes a knowledge of nonstandard analysis.
reviewed by: Paul Vojta
Mathematics Subject Classification ID: 11U10
Mathematics Subject Classification ID: 03H15
Mathematics Subject Classification ID: 11D75
Mathematics Subject Classification ID: 11J68
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14G25
zbMATH DE Number: 8528
zbMATH Keywords: Siegel's theorem
zbMATH Keywords: affine curves
zbMATH Keywords: integral points
zbMATH Keywords: Roth's theorem
zbMATH Keywords: nonstandard analysis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 8528