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.
Accepté le :
Publié le :
DOI : 10.5802/jep.33
Mot clés : Inégalité d’indice de Hodge, géométrie d’Arakelov, diviseur adélique, corps d’Okounkov, système linéaire gradué, $\mathbb{R}$-filtration
Keywords: Hodge index inequality, Arakelov geometry, adelic divisor, Okounkov body, graded linear series, $\mathbb{R}$-filtration
Huayi Chen 1
CC-BY-ND 4.0
@article{JEP_2016__3__231_0,
author = {Huayi Chen},
title = {In\'egalit\'e d{\textquoteright}indice de {Hodge} en g\'eom\'etrie et arithm\'etique~: une approche probabiliste},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {231--262},
publisher = {ole polytechnique},
volume = {3},
year = {2016},
doi = {10.5802/jep.33},
zbl = {06670707},
mrnumber = {3522823},
language = {fr},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.33/}
}
TY - JOUR AU - Huayi Chen TI - Inégalité d’indice de Hodge en géométrie et arithmétique : une approche probabiliste JO - Journal de l’École polytechnique — Mathématiques PY - 2016 SP - 231 EP - 262 VL - 3 PB - ole polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.33/ DO - 10.5802/jep.33 LA - fr ID - JEP_2016__3__231_0 ER -
%0 Journal Article %A Huayi Chen %T Inégalité d’indice de Hodge en géométrie et arithmétique : une approche probabiliste %J Journal de l’École polytechnique — Mathématiques %D 2016 %P 231-262 %V 3 %I ole polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.33/ %R 10.5802/jep.33 %G fr %F JEP_2016__3__231_0
Huayi Chen. 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/articles/10.5802/jep.33/
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