Un théorème de linéarité de la construction d'Abbes et Saito pour les connexions méromorphes

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Let M be a connection on a complex affine space with poles along a hyperplane. In this paper, we prove that the nearby cycles of Abbes and Saito's construction applied to M satisfy a linearity condition analogous to that obtained by Abbes and Saito in the l-adic setting. This generalizes the fact that in dimension one, the module produced by Abbes and Saito's construction is a direct sum of exponential modules associated to linear forms.