Approximation of adelic divisors and equidistribution of small points
Abstract
We study the asymptotic distribution of the Galois orbits of generic sequences of algebraic points of small height in a projective variety over a number field. Our main result is a generalization of Yuan’s equidistribution theorem that applies to heights for which Zhang’s lower bound for the essential minimum is not necessarily an equality. It extends to all projective varieties a theorem of Burgos Gil, Philippon, Rivera-Letelier and the second author for toric varieties. It also applies to sums of canonical heights for an algebraic dynamical system, and in particular it recovers Kühne’s semiabelian equidistribution theorem. We also generalize previous work of Chambert-Loir and Thuillier to obtain new logarithmic equidistribution results. Finally we extend our main result to the quasi-projective setting recently introduced by Yuan and Zhang.
Related
- Adelic points and unmramified Brauer approximation for classifying stacks
- Equidistribution of small points over finitely generated fields
- Effective Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces
- Equidistribution of saddle periodic points for automorphisms on compact Kähler manifolds
- Naturalization of Vinti's intermediary orbit---or how to get rid of small divisors in Brouwer's satellite solution
BibTeX
@article{ballay2026approximation,
title = {{Approximation of adelic divisors and equidistribution of small points}},
author = {François Ballaÿ and Martín Sombra},
journal = {Inventiones Mathematicae},
year = {2026},
month = oct,
doi = {10.1007/s00222-026-01456-y},
url = {https://hal.science/hal-05779091v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Approximation of adelic divisors and equidistribution of small points
AU - François Ballaÿ
AU - Martín Sombra
PY - 2026
DA - 2026/10/05
JO - Inventiones Mathematicae
DO - 10.1007/s00222-026-01456-y
UR - https://hal.science/hal-05779091v1
AB - We study the asymptotic distribution of the Galois orbits of generic sequences of algebraic points of small height in a projective variety over a number field. Our main result is a generalization of Yuan’s equidistribution theorem that applies to heights for which Zhang’s lower bound for the essential minimum is not necessarily an equality. It extends to all projective varieties a theorem of Burgos Gil, Philippon, Rivera-Letelier and the second author for toric varieties. It also applies to sums of canonical heights for an algebraic dynamical system, and in particular it recovers Kühne’s semiabelian equidistribution theorem. We also generalize previous work of Chambert-Loir and Thuillier to obtain new logarithmic equidistribution results. Finally we extend our main result to the quasi-projective setting recently introduced by Yuan and Zhang.
SN - 0020-9910
SN - 1432-1297
ER -