The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and the equidistribution of these is a far less explored topic.
In this paper, we introduce a new notion of higher dimensional essential minimum and use it to prove equidistribution of generic and small effective cycles. The latter generalizes the previous higher dimensional equidistribution theorems by considering cycles and by allowing more flexibility on the arithmetic datum.
Le minimum essentiel et l’équirépartition des petits points sont deux sujets entrelacés et bien établis en géométrie arithmétique. Cependant, on manque d’un analogue pour le minimum essentiel pour des sous-variétés de dimension supérieure, et l’équirépartition de celles-ci est un sujet beaucoup moins exploré.
Dans cet article, on introduit une nouvelle notion de minimum essentiel de dimension supérieure et on l’utilise pour prouver un résultat d’équirépartition pour des cycles effectifs. Celui-ci généralise les théorèmes d’équirépartition de dimension supérieure précédents en permettant plus de flexibilité sur les données arithmétiques.
Revised:
Accepted:
Published online:
Keywords: Equidistribution of cycles, Arakelov geometry, Heights, Essential minimum
Mot clés : Équirépartition de cycles, Géométrie d’Arakelov, Hauteurs, Minimum essentiel
Gualdi, Roberto 1; Martínez, César 1
@article{AIF_2022__72_4_1329_0, author = {Gualdi, Roberto and Mart{\'\i}nez, C\'esar}, title = {Higher dimensional essential minima and equidistribution of cycles}, journal = {Annales de l'Institut Fourier}, pages = {1329--1377}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {4}, year = {2022}, doi = {10.5802/aif.3500}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3500/} }
TY - JOUR AU - Gualdi, Roberto AU - Martínez, César TI - Higher dimensional essential minima and equidistribution of cycles JO - Annales de l'Institut Fourier PY - 2022 SP - 1329 EP - 1377 VL - 72 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3500/ DO - 10.5802/aif.3500 LA - en ID - AIF_2022__72_4_1329_0 ER -
%0 Journal Article %A Gualdi, Roberto %A Martínez, César %T Higher dimensional essential minima and equidistribution of cycles %J Annales de l'Institut Fourier %D 2022 %P 1329-1377 %V 72 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3500/ %R 10.5802/aif.3500 %G en %F AIF_2022__72_4_1329_0
Gualdi, Roberto; Martínez, César. Higher dimensional essential minima and equidistribution of cycles. Annales de l'Institut Fourier, Volume 72 (2022) no. 4, pp. 1329-1377. doi : 10.5802/aif.3500. https://aif.centre-mersenne.org/articles/10.5802/aif.3500/
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