We prove that the k-truncated microsupport of the specialization of a complex of sheaves F along a submanifold is contained in the normal cone to the conormal bundle along the k-truncated microsupport of F. In the complex case, applying our estimates to F = RHom D (M, O), where M is a coherent D-module, we obtain new estimates for the truncated microsupport… (More)
The notion of microsupport and regularity for ind-sheaves was introduced by M. Kashiwara and P. Schapira in . In this paper we study the behaviour of the microsupport under several functorial operations and characterize " microlocally " the ind-sheaves that are regular along involutive manifolds. As an application we prove that if a coherent D-module M… (More)
Let X be a complex manifold. In  M. Kashiwara and P. Schapira made the conjecture that a holonomic D X-module M is regular holo-nomic if and only if RIhom βX DX (β X M, O t X) is regular (in the sense of ), the " only if " part of this conjecture following immediately from . Our aim is to prove this conjecture in dimension one.