[Solutions holomorphes tempérées des -modules sur les courbes complexes et invariants formels]
Soit une courbe analytique complexe. Dans cet article nous démontrons que le faisceau sous-analytique des solutions holomorphes tempérées des -modules sur induit un foncteur pleinement fidèle sur une sous-catégorie des germes des -modules holonomes formels. De plus, étant donné un germe de -module holonome, nous obtenons des résultats qui lient le faisceau sous-analytique des solutions tempérées de avec les invariants formels et analytiques classiques de .
Let be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of -modules on induces a fully faithful functor on a subcategory of germs of formal holonomic -modules. Further, given a germ of holonomic -module, we obtain some results linking the subanalytic sheaf of tempered solutions of and the classical formal and analytic invariants of .
Keywords: $\mathcal{D}$-modules, irregular singularities, tempered holomorphic functions, subanalytic
Mot clés : $\mathcal{D}$-modules, singularités irréguliers, fonctions holomorphes tempérées, sous-analytique
@article{AIF_2009__59_4_1611_0,
author = {Morando, Giovanni},
title = {Tempered solutions of $\mathcal{D}$-modules on complex curves and formal invariants},
journal = {Annales de l'Institut Fourier},
pages = {1611--1639},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {59},
number = {4},
year = {2009},
doi = {10.5802/aif.2472},
mrnumber = {2566969},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2472/}
}
TY - JOUR
AU - Morando, Giovanni
TI - Tempered solutions of $\mathcal{D}$-modules on complex curves and formal invariants
JO - Annales de l'Institut Fourier
PY - 2009
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EP - 1639
VL - 59
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PB - Association des Annales de l’institut Fourier
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DO - 10.5802/aif.2472
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Morando, Giovanni. Tempered solutions of $\mathcal{D}$-modules on complex curves and formal invariants. Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1611-1639. doi : 10.5802/aif.2472. http://archive.numdam.org/articles/10.5802/aif.2472/
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