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September 2019 Borne de hauteur semi-effective pour le problème de Mordell-Lang dans un tore
Jérôme Von Buhren
Funct. Approx. Comment. Math. 61(1): 109-120 (September 2019). DOI: 10.7169/facm/1779

Abstract

If $X$ is a closed subscheme of torus $\mathbb{G}_{m,K}^g$ on a number field $K$, we define $Z_X$ as the union of all translated positive dimensional subtori contained in $X$. Vojta proved that the set of integral points on $X\setminus Z_X$ is finite. In this article, we consider a family of closed subschemes $V\to P$ of $\mathbb{G}_{m,K}^g$. We prove a semi-effective bound for the height of the integer points in $V_p\setminus Z_{V_p}$. We prove this result in the more general context of the Mordell-Lang plus Bogomolov problem and we obtain a corollary on the unit equation.

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Jérôme Von Buhren. "Borne de hauteur semi-effective pour le problème de Mordell-Lang dans un tore." Funct. Approx. Comment. Math. 61 (1) 109 - 120, September 2019. https://doi.org/10.7169/facm/1779

Information

Published: September 2019
First available in Project Euclid: 29 November 2018

zbMATH: 07126913
MathSciNet: MR4012365
Digital Object Identifier: 10.7169/facm/1779

Subjects:
Primary: 11G35, 11G50, 14G05

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.61 • No. 1 • September 2019
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