[Construction élémentaire des courants résiduels associés aux idéaux Cohen–Macaulay]
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.
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Keywords: residue currents, explicit construction, theory of integral representations, duality principle, Cohen–Macaulay ideals
Mot 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{\textendash}Macaulay} ideals},
journal = {Annales de l'Institut Fourier},
pages = {377--391},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {68},
number = {1},
year = {2018},
doi = {10.5802/aif.3164},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3164/}
}
TY - JOUR AU - Lärkäng, Richard AU - Mazzilli, Emmanuel TI - Elementary construction of residue currents associated to Cohen–Macaulay ideals JO - Annales de l'Institut Fourier PY - 2018 SP - 377 EP - 391 VL - 68 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3164/ DO - 10.5802/aif.3164 LA - en ID - AIF_2018__68_1_377_0 ER -
%0 Journal Article %A Lärkäng, Richard %A Mazzilli, Emmanuel %T Elementary construction of residue currents associated to Cohen–Macaulay ideals %J Annales de l'Institut Fourier %D 2018 %P 377-391 %V 68 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3164/ %R 10.5802/aif.3164 %G en %F 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://www.numdam.org/articles/10.5802/aif.3164/
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