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, Volume 3  (2016), p. 231-262

By using the probabilistic approach in arithmetic geometry, one gives a new proof of the Hodge index inequality for adelic -divisors, and proposes a new way of generalizing it to higher dimensional case.

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

Received : 2015-03-31
Accepted : 2016-06-25
Published online : 2016-07-11
DOI : https://doi.org/10.5802/jep.33
Classification:  14G40,  11G30
Keywords: Hodge index inequality, Arakelov geometry, adelic divisor, Okounkov body, graded linear series, -filtration
@article{JEP_2016__3__231_0,
     author = {Chen, Huayi},
     title = {In\'egalit\'e d'indice de Hodge en g\'eom\'etrie et arithm\'etique~: une approche probabiliste},
     journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
     publisher = {ole polytechnique},
     volume = {3},
     year = {2016},
     pages = {231-262},
     doi = {10.5802/jep.33},
     mrnumber = {3522823},
     zbl = {06670707},
     language = {fr},
     url = {http://www.numdam.org/item/JEP_2016__3__231_0}
}
Chen, Huayi. Inégalité d’indice de Hodge en géométrie et arithmétique : une approche probabiliste. Journal de l’École polytechnique - Mathématiques, Volume 3 (2016) , pp. 231-262. doi : 10.5802/jep.33. http://www.numdam.org/item/JEP_2016__3__231_0/

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