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

Jean-Baptiste Teyssier (1)

1 Institut für Informatik [Berlin]

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.

Mots clés: D-modules; nearby cycle; Malgrange lattice

Domaines: Géométrie algébrique [math.AG]

Jean-Baptiste Teyssier. Un théorème de linéarité de la construction d'Abbes et Saito pour les connexions méromorphes.. 2014. ⟨hal-00969296⟩