Translator Disclaimer
2020 Tubular approaches to Baker's method for curves and varieties
Samuel Le Fourn
Algebra Number Theory 14(3): 763-785 (2020). DOI: 10.2140/ant.2020.14.763

Abstract

Baker’s method, relying on estimates on linear forms in logarithms of algebraic numbers, allows one to prove in several situations the effective finiteness of integral points on varieties. In this article, we generalize results of Levin regarding Baker’s method for varieties, and explain how, quite surprisingly, it mixes (under additional hypotheses) with Runge’s method to improve some known estimates in the case of curves by bypassing (or more generally reducing) the need for linear forms in p-adic logarithms. We then use these ideas to improve known estimates on solutions of S-unit equations. Finally, we explain how a finer analysis and formalism can improve upon the conditions given, and give some applications to the Siegel modular variety A2(2).

Citation

Download Citation

Samuel Le Fourn. "Tubular approaches to Baker's method for curves and varieties." Algebra Number Theory 14 (3) 763 - 785, 2020. https://doi.org/10.2140/ant.2020.14.763

Information

Received: 18 February 2019; Revised: 20 August 2019; Accepted: 7 October 2019; Published: 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4113780
Digital Object Identifier: 10.2140/ant.2020.14.763

Subjects:
Primary: 11G35
Secondary: 11J86

Keywords: $S$-unit equation , Baker's method , Integral points , Runge's method

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.14 • No. 3 • 2020
MSP
Back to Top