Work

Nombre De Petits Points Sur Une Variété Abélienne

Year: 2025

Type: article

Abstract: Given a polarised abelian variety over a number field, we provide totally explicit upper bounds for the cardinality of the rational points whose Néron-Tate height is less than a small threshold. These imply new estimates for the number of torsion points as well as the minimal height of a non-torsion point. Our bounds involve the Faltings height and dimension of the abelian variety together with the degrees of the polarisation and the number field but we also get a stronger statement where we use certain successive minima associated to the period lattice at a fixed archimedean place, in the spirit of a result of David for elliptic curves.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748024000549

Authors: Éric Gaudron, Gaël Rémond

Institutions: Centre National de la Recherche Scientifique, Université Clermont Auvergne, Laboratoire de Mathématiques Blaise Pascal, Institut National des Sciences Mathématiques et de leurs Interactions, Institut Fourier

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4392890726

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Cites: 32

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Related to: 10