Approches courantielles à la Mellin dans un cadre non archimédien
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 2, pp. 357-396.

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 j U au-dessus d’un ouvert U d’un bon espace de Berkovich, lorsque chaque j est équipé d’une métrique lisse et que codim U ( jJ Supp[div(s j )])#J pour tout ensemble J{1,,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.

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 j U over an open U in a good Berkovich space when each j has a smooth metric and codim U ( jJ Supp[div(s j )])#J for every set J{1,,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.

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Accepté le :
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DOI : https://doi.org/10.5802/afst.1602
Classification : 32U25,  32U35,  32U40,  14G22,  14G40,  14TXX
Mots clés : courants, diviseurs, équations de Lelong–Poincaré, formule de King, nombres de Lelong
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     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},
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Hamidine, Ibrahima. Approches courantielles à la Mellin dans un cadre non archimédien. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 2, pp. 357-396. doi : 10.5802/afst.1602. http://archive.numdam.org/articles/10.5802/afst.1602/

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