no. 4
Tempered solutions of 𝒟-modules on complex curves and formal invariants
[Solutions holomorphes tempérées des 𝒟-modules sur les courbes complexes et invariants formels]
Morando, Giovanni1
1 Università di Padova Dipartimento di Matematica Pura ed Applicata Via Trieste 63 35121 Padova (Italy) and Universidade de Lisboa Centro de Álgebra Av. Prof. Gama Pinto, 2 1649-003 Lisboa (Portugal)
Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1611-1639.

Soit X une courbe analytique complexe. Dans cet article nous démontrons que le faisceau sous-analytique des solutions holomorphes tempérées des 𝒟-modules sur X induit un foncteur pleinement fidèle sur une sous-catégorie des germes des 𝒟-modules holonomes formels. De plus, étant donné un germe ℳ de 𝒟-module holonome, nous obtenons des résultats qui lient le faisceau sous-analytique des solutions tempérées de ℳ avec les invariants formels et analytiques classiques de ℳ.

Let X be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of 𝒟-modules on X induces a fully faithful functor on a subcategory of germs of formal holonomic 𝒟-modules. Further, given a germ ℳ of holonomic 𝒟-module, we obtain some results linking the subanalytic sheaf of tempered solutions of ℳ and the classical formal and analytic invariants of ℳ.

DOI : 10.5802/aif.2472
Classification : 34M35, 32B20, 34Mxx
Keywords: $\mathcal{D}$-modules, irregular singularities, tempered holomorphic functions, subanalytic
Mot clés : $\mathcal{D}$-modules, singularités irréguliers, fonctions holomorphes tempérées, sous-analytique

Morando, Giovanni 1

1 Università di Padova Dipartimento di Matematica Pura ed Applicata Via Trieste 63 35121 Padova (Italy) and Universidade de Lisboa Centro de Álgebra Av. Prof. Gama Pinto, 2 1649-003 Lisboa (Portugal) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2472/

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