Elementary construction of residue currents associated to Cohen–Macaulay ideals  [ Construction élémentaire des courants résiduels associés aux idéaux Cohen–Macaulay ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 377-391.

Pour un idéal Cohen–Macaulay de fonctions holomorphes, nous construisons de manière élémentaire des courants résiduels qui s’annulent précisément sur cet idéal. Nous donnons deux constructions, l’une utilisant la théorie des idéaux en algèbre commutative, et l’autre utilisant des représentations intégrales qui donnent une décomposition dans l’idéal modulo ces courants résiduels.

For a Cohen–Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the theory of linkage, and another using an explicit division formula involving these residue currents to express the ideal membership.

Reçu le : 2016-07-09
Révisé le : 2017-05-21
Accepté le : 2017-06-25
Publié le : 2018-04-17
DOI : https://doi.org/10.5802/aif.3164
Classification : 32A26,  32A27,  32C30,  32C37,  13C14
Mots clés : courants résiduels, construction explicite, théorie des représentations intégrales, principe de dualité, idéaux Cohen–Macaulay
@article{AIF_2018__68_1_377_0,
     author = {L\"ark\"ang, Richard and Mazzilli, Emmanuel},
     title = {Elementary construction of residue currents associated to Cohen--Macaulay ideals},
     journal = {Annales de l'Institut Fourier},
     pages = {377--391},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {1},
     year = {2018},
     doi = {10.5802/aif.3164},
     language = {en},
     url = {archive.numdam.org/item/AIF_2018__68_1_377_0/}
}
Lärkäng, Richard; Mazzilli, Emmanuel. Elementary construction of residue currents associated to Cohen–Macaulay ideals. Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 377-391. doi : 10.5802/aif.3164. http://archive.numdam.org/item/AIF_2018__68_1_377_0/

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