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Approches courantielles à la Mellin dans un cadre non archimédien
[Mellin’s Currential approaches in a non archimedean framework]
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 2, pp. 357-396.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1602
Classification: 32U25,  32U35,  32U40,  14G22,  14G40,  14TXX
Keywords: currents, divisors, Lelong–Poincaré equations, King formula, Lelong numbers
Ibrahima Hamidine 1

1 Département de Mathématiques, UFR Sciences et Technologies, Université Assane Seck de Ziguinchor, BP : 523, Sénégal
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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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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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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