Greatest common divisors and Vojta's conjecture for blowups of algebraic tori
type: Item
instance of: scholarly article
title: Greatest common divisors and Vojta's conjecture for blowups of algebraic tori
zbMATH Open document ID: 1437.11094
author: Aaron Levin
published in: Inventiones Mathematicae
publication date: 2019-02-14T00:00:00Z
review text: In the paper under review, the author gives an inequality bounding the greatest common divisor of multivariate polynomials evaluated at \({\mathcal S}\)-unit arguments. The author's result extends the well-known result of Bugeaud, Corvaja and Zannier [\textit{Y. Bugeaud} et al., Math. Z. 243, No. 1, 79--84 (2003; Zbl 1021.11001)] on the greatest common divisor of \(a^n-1\) and \(b^n-1\) for multiplicatively independent integers \(a>1\) and \(b>1\) as well as its generalizations by Corvaja and Zanier, Fuchs, and Hernández and the reviewer. As related results, following ideas of Silverman, the author also proves special cases of Volta's conjectures for blow-ups of toric varieties. Finally, the author classifies when members of linear recurrent sequences with simple roots may have a ``large'' greatest common divisor infinitely often. The main tool is Schmidt's subspace theorem from Diophantine approximations.
reviewed by: Florian Luca
Mathematics Subject Classification ID: 11J25
Mathematics Subject Classification ID: 11G35
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 7023767
zbMATH Keywords: recurrences
zbMATH Keywords: Vojta's conjecture
zbMATH Keywords: applications of subspace theorem
Wikidata QID: Q123231128
MaRDI profile type: Publication
full work available at URL: s00222-018-0831-z
OpenAlex ID: W2895473295
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DOI: 10.1007/S00222-018-0831-Z
description: scientific article; zbMATH DE number 7023767