Effective equidistribution of S-integral points on symmetric varieties

[Équidistribution effective des points S-entiers des variétés symétriques]

Benoist, Yves ; Oh, Hee

Annales de l'Institut Fourier, Tome 62 (2012), p. 1889-1942 / Harvested from Numdam

Résumé

Soit $K$ un corps global de caractéristique différente de 2. Soit $\bf {Z}=\bf {H}\backslash \bf {G}$ une variété symétrique définie sur $K$ et $S$ un ensemble fini de places de $K$. Nous obtenons des résultats de comptage et d’équidistribution pour les points S-entiers de $\bf {Z}$. Nos résultats sont effectifs quand $K$ est un corps de nombre.

Abstract

Let $K$ be a global field of characteristic not 2. Let $\bf {Z}=\bf {H}\backslash \bf {G}$ be a symmetric variety defined over $K$ and $S$ a finite set of places of $K$. We obtain counting and equidistribution results for the S-integral points of $\bf {Z}$. Our results are effective when $K$ is a number field.

Détail

Publié le : 2012-01-01

MR 3025156 | Zbl pre06130496

DOI : https://doi.org/10.5802/aif.2738
Classification:  11G35 11S82 14G05 22E40 37A25 37P30
Mots clés: Comptage, équidistribution, points rationnels, mélange, espaces symétriques, décomposition polaire, résolution des singularités.

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