Inégalité d’indice de Hodge en géométrie et arithmétique : une approche probabiliste
Journal de l’École polytechnique — Mathématiques, Tome 3 (2016) , pp. 231-262.

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.

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.

Reçu le : 2015-03-31
Accepté le : 2016-06-25
Publié le : 2016-07-11
DOI : https://doi.org/10.5802/jep.33
Classification : 14G40,  11G30
Mots clés: Inégalité d’indice de Hodge, géométrie d’Arakelov, diviseur adélique, corps d’Okounkov, système linéaire gradué, -filtration
@article{JEP_2016__3__231_0,
     author = {Huayi Chen},
     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},
     pages = {231--262},
     publisher = {ole polytechnique},
     volume = {3},
     year = {2016},
     doi = {10.5802/jep.33},
     zbl = {06670707},
     mrnumber = {3522823},
     language = {fr},
     url = {jep.centre-mersenne.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, Tome 3 (2016) , pp. 231-262. doi : 10.5802/jep.33. https://jep.centre-mersenne.org/item/JEP_2016__3__231_0/

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