Approches courantielles à la Mellin dans un cadre non archimédien

Ibrahima Hamidine

doi:10.5802/afst.1602

Approches courantielles à la Mellin dans un cadre non archimédien
[Mellin’s Currential approaches in a non archimedean framework]

Ibrahima Hamidine ¹

¹ Département de Mathématiques, UFR Sciences et Technologies, Université Assane Seck de Ziguinchor, BP : 523, Sénégal

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 2, pp. 357-396.

Abstract
Abstract

We propose an approach of Mellin type for the approximation of integration currents or the effective realization of normalized Green currents associated with a cycle $⋀_{1}^{m} [div (s_{j})]$ , where $s_{j}$ is a meromorphic section of a line bundle $ℒ_{j} \to U$ over an open $U$ in a good Berkovich space when each $ℒ_{j}$ has a smooth metric and ${codim}_{U} (⋂_{j \in J} Supp [div (s_{j})]) \geq # J$ for every set $J \subset {1, \dots, p}$ . We also study the transposition to the non archimedean context of Crofton and King formulas, particularly the approximate realization of Vogel and Segre currents.

On propose une approche du type Mellin pour l’approximation des courants d’intégration ou la réalisation effective de courants de Green normalisés associés à un cycle $⋀_{1}^{m} [div (s_{j})]$ , où $s_{j}$ est une section méromorphe d’un fibré en droites $ℒ_{j} \to U$ au-dessus d’un ouvert $U$ d’un bon espace de Berkovich, lorsque chaque $ℒ_{j}$ est équipé d’une métrique lisse et que ${codim}_{U} (⋂_{j \in J} Supp [div (s_{j})]) \geq # J$ pour tout ensemble $J \subset {1, \dots, p}$ . On étudie aussi la transposition au cadre non archimédien des formules de Crofton et de King, en particulier la réalisation approchée de courants de Vogel et de Segre.

Received: 2016-04-07
Accepted: 2017-05-22
Published online: 2019-05-02

MR Zbl

DOI: 10.5802/afst.1602

Classification: 32U25, 32U35, 32U40, 14G22, 14G40, 14TXX
Mot clés : courants, diviseurs, équations de Lelong–Poincaré, formule de King, nombres de Lelong
Keywords: currents, divisors, Lelong–Poincaré equations, King formula, Lelong numbers

Author's affiliations:

Ibrahima Hamidine ¹

¹ Département de Mathématiques, UFR Sciences et Technologies, Université Assane Seck de Ziguinchor, BP : 523, Sénégal

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Ibrahima Hamidine},
     title = {Approches courantielles \`a la {Mellin} dans un cadre non archim\'edien},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {357--396},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 28},
     number = {2},
     year = {2019},
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Ibrahima Hamidine. Approches courantielles à la Mellin dans un cadre non archimédien. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 2, pp. 357-396. doi : 10.5802/afst.1602. https://afst.centre-mersenne.org/articles/10.5802/afst.1602/

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