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Huayi Chen
Inégalité d’indice de Hodge en géométrie et arithmétique : une approche probabiliste
(Hodge index inequality in geometry and arithmetic: a probabilistic approach)
Journal de l'École polytechnique — Mathématiques, 3 (2016), p. 231-262, doi: 10.5802/jep.33
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Class. Math.: 14G40, 11G30
Mots clés: Inégalité d’indice de Hodge, géométrie d’Arakelov, diviseur adélique, corps d’Okounkov, système linéaire gradué, $\mathbb{R}$-filtration

Résumé - Abstract

En utilisant l’approche probabiliste en géométrie arithmétique, nous donnons une nouvelle démonstration de l’inégalité d’indice de Hodge pour les $\mathbb{R}$-diviseurs adéliques, et nous proposons une nouvelle voie pour sa généralisation au cas de dimension supérieure.

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