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), pp. 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.

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Accepted:
Published online:
DOI: 10.5802/jep.33
Classification: 14G40,  11G30
Keywords: Hodge index inequality, Arakelov geometry, adelic divisor, Okounkov body, graded linear series, -filtration
Chen, Huayi 1

1 Université Grenoble Alpes, Institut Fourier F-38000 Grenoble, France
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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/articles/10.5802/jep.33/

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