TY - JOUR

T1 - Generalized Vojta-Rémond inequality

AU - Dill, Gabriel A.

N1 - Funding Information: I thank Thomas Ange for sharing his unpublished work. I thank my advisor Philipp Habegger for his continuous encouragement and for many helpful and interesting discussions. I thank Philipp Habegger and Gaël Rémond for helpful comments on a preliminary version of this paper. I thank the anonymous referee for their comments, which helped me to improve the exposition and led to a strengthening of the main result. This work was supported by the Swiss National Science Foundation as part of the project “Diophantine Problems, o-Minimality, and Heights”, no. 200021 165525. Publisher Copyright: © 2020 World Scientific Publishing Company.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Following and generalizing unpublished work of Ange, we prove a generalized version of Rémond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective varieties, defined over the field of algebraic numbers, instead of powers of one fixed such variety. The proof runs closely along the lines of Rémond's proof.

AB - Following and generalizing unpublished work of Ange, we prove a generalized version of Rémond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective varieties, defined over the field of algebraic numbers, instead of powers of one fixed such variety. The proof runs closely along the lines of Rémond's proof.

KW - arithmetic geometry

KW - diophantine approximation

KW - Heights

UR - http://www.scopus.com/inward/record.url?scp=85070273679&partnerID=8YFLogxK

U2 - 10.1142/S1793042120500062

DO - 10.1142/S1793042120500062

M3 - Article

AN - SCOPUS:85070273679

VL - 16

SP - 107

EP - 120

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 1

ER -